About the project

This seems very interesting course, I am much excited day after day about its potentials and applications!

My Github repository is here


Regression and model validation

Here we practice Data management and wrangling as well as linear Regression model creation and analysis.

Our data set from Data wrangling will be used, R script for Data wrangling can be found here

Reading students2014 data, Explore the structure and the dimensions of the data

read.csv (file = "C:/Users/ahmed/Desktop/IODS-project/data/learning2014_AGA.csv")
##       X gender Age Attitude     deep  stra     surf Points
## 1     1      F  53       37 3.583333 3.375 2.583333     25
## 2     2      M  55       31 2.916667 2.750 3.166667     12
## 3     3      F  49       25 3.500000 3.625 2.250000     24
## 4     4      M  53       35 3.500000 3.125 2.250000     10
## 5     5      M  49       37 3.666667 3.625 2.833333     22
## 6     6      F  38       38 4.750000 3.625 2.416667     21
## 7     7      M  50       35 3.833333 2.250 1.916667     21
## 8     8      F  37       29 3.250000 4.000 2.833333     31
## 9     9      M  37       38 4.333333 4.250 2.166667     24
## 10   10      F  42       21 4.000000 3.500 3.000000     26
## 11   11      M  37       39 3.583333 3.625 2.666667     31
## 12   12      F  34       38 3.833333 4.750 2.416667     31
## 13   13      F  34       24 4.250000 3.625 2.250000     23
## 14   14      F  34       30 3.333333 3.500 2.750000     25
## 15   15      M  35       26 4.166667 1.750 2.333333     21
## 16   16      F  33       41 3.666667 3.875 2.333333     31
## 17   17      F  32       26 4.083333 1.375 2.916667     20
## 18   18      F  44       26 3.500000 3.250 2.500000     22
## 19   19      M  29       17 4.083333 3.000 3.750000      9
## 20   20      F  30       27 4.000000 3.750 2.750000     24
## 21   21      M  27       39 3.916667 2.625 2.333333     28
## 22   22      M  29       34 4.000000 2.375 2.416667     30
## 23   23      F  31       27 4.000000 3.625 3.000000     24
## 24   24      F  37       23 3.666667 2.750 2.416667      9
## 25   25      F  26       37 3.666667 1.750 2.833333     26
## 26   26      F  26       44 4.416667 3.250 3.166667     32
## 27   27      M  30       41 3.916667 4.000 3.000000     32
## 28   28      F  33       37 3.750000 3.625 2.000000     33
## 29   29      F  33       25 3.250000 2.875 3.500000     29
## 30   30      M  28       30 3.583333 3.000 3.750000     30
## 31   31      M  26       34 4.916667 1.625 2.500000     19
## 32   32      F  27       32 3.583333 3.250 2.083333     23
## 33   33      F  25       20 2.916667 3.500 2.416667     19
## 34   34      F  31       24 3.666667 3.000 2.583333     12
## 35   35      M  20       42 4.500000 3.250 1.583333     10
## 36   36      F  39       16 4.083333 1.875 2.833333     11
## 37   37      M  38       31 3.833333 4.375 1.833333     20
## 38   38      M  24       38 3.250000 3.625 2.416667     26
## 39   39      M  26       38 2.333333 2.500 3.250000     31
## 40   40      M  25       33 3.333333 1.250 3.416667     20
## 41   41      F  30       17 4.083333 4.000 3.416667     23
## 42   42      F  25       25 2.916667 3.000 3.166667     12
## 43   43      M  30       32 3.333333 2.500 3.500000     24
## 44   44      F  48       35 3.833333 4.875 2.666667     17
## 45   45      F  24       32 3.666667 5.000 2.416667     29
## 46   46      F  40       42 4.666667 4.375 3.583333     23
## 47   47      M  25       31 3.750000 3.250 2.083333     28
## 48   48      F  23       39 3.416667 4.000 3.750000     31
## 49   49      F  25       19 4.166667 3.125 2.916667     23
## 50   50      F  23       21 2.916667 2.500 2.916667     25
## 51   51      M  27       25 4.166667 3.125 2.416667     18
## 52   52      M  25       32 3.583333 3.250 3.000000     19
## 53   53      M  23       32 2.833333 2.125 3.416667     22
## 54   54      F  23       26 4.000000 2.750 2.916667     25
## 55   55      F  23       23 2.916667 2.375 3.250000     21
## 56   56      F  45       38 3.000000 3.125 3.250000      9
## 57   57      F  22       28 4.083333 4.000 2.333333     28
## 58   58      F  23       33 2.916667 4.000 3.250000     25
## 59   59      M  21       48 3.500000 2.250 2.500000     29
## 60   60      M  21       40 4.333333 3.250 1.750000     33
## 61   61      F  21       40 4.250000 3.625 2.250000     33
## 62   62      F  21       47 3.416667 3.625 2.083333     25
## 63   63      F  26       23 3.083333 2.500 2.833333     18
## 64   64      F  25       31 4.583333 1.875 2.833333     22
## 65   65      F  26       27 3.416667 2.000 2.416667     17
## 66   66      M  21       41 3.416667 1.875 2.250000     25
## 67   67      F  23       34 3.416667 4.000 2.833333     28
## 68   68      F  22       25 3.583333 2.875 2.250000     22
## 69   69      F  22       21 1.583333 3.875 1.833333     26
## 70   70      F  22       14 3.333333 2.500 2.916667     11
## 71   71      F  23       19 4.333333 2.750 2.916667     29
## 72   72      M  22       37 4.416667 4.500 2.083333     22
## 73   73      M  23       32 4.833333 3.375 2.333333     21
## 74   74      M  24       28 3.083333 2.625 2.416667     28
## 75   75      F  22       41 3.000000 4.125 2.750000     33
## 76   76      F  23       25 4.083333 2.625 3.250000     16
## 77   77      M  22       28 4.083333 2.250 1.750000     31
## 78   78      M  20       38 3.750000 2.750 2.583333     22
## 79   79      M  22       31 3.083333 3.000 3.333333     31
## 80   80      M  21       35 4.750000 1.625 2.833333     23
## 81   81      F  22       36 4.250000 1.875 2.500000     26
## 82   82      F  23       26 4.166667 3.375 2.416667     12
## 83   83      M  21       44 4.416667 3.750 2.416667     26
## 84   84      M  22       45 3.833333 2.125 2.583333     31
## 85   85      M  29       32 3.333333 2.375 3.000000     19
## 86   86      F  29       39 3.166667 2.750 2.000000     30
## 87   87      F  21       25 3.166667 3.125 3.416667     12
## 88   88      M  28       33 3.833333 3.500 2.833333     17
## 89   89      F  21       33 4.250000 2.625 2.250000     18
## 90   90      F  30       30 3.833333 3.375 2.750000     19
## 91   91      F  21       29 3.666667 2.250 3.916667     21
## 92   92      M  23       33 3.833333 3.000 2.333333     24
## 93   93      F  21       33 3.833333 4.000 2.750000     28
## 94   94      F  21       35 3.833333 3.500 2.750000     17
## 95   95      F  20       36 3.666667 2.625 2.916667     18
## 96   96      M  22       37 4.333333 2.500 2.083333     17
## 97   97      M  21       42 3.750000 3.750 3.666667     23
## 98   98      M  21       32 4.166667 3.625 2.833333     26
## 99   99      F  20       50 4.000000 4.125 3.416667     28
## 100 100      M  22       47 4.000000 4.375 1.583333     31
## 101 101      F  20       36 4.583333 2.625 2.916667     27
## 102 102      F  20       36 3.666667 4.000 3.000000     25
## 103 103      M  24       29 3.666667 2.750 2.916667     23
## 104 104      F  20       35 3.833333 2.750 2.666667     21
## 105 105      F  19       40 2.583333 1.375 3.000000     27
## 106 106      F  21       35 3.500000 2.250 2.750000     28
## 107 107      F  21       32 3.083333 3.625 3.083333     23
## 108 108      F  22       26 4.250000 3.750 2.500000     21
## 109 109      F  25       20 3.166667 4.000 2.333333     25
## 110 110      F  21       27 3.083333 3.125 3.000000     11
## 111 111      F  22       32 4.166667 3.250 3.000000     19
## 112 112      F  25       33 2.250000 2.125 4.000000     24
## 113 113      F  20       39 3.333333 2.875 3.250000     28
## 114 114      M  24       33 3.083333 1.500 3.500000     21
## 115 115      F  20       30 2.750000 2.500 3.500000     24
## 116 116      M  21       37 3.250000 3.250 3.833333     24
## 117 117      F  20       25 4.000000 3.625 2.916667     20
## 118 118      F  20       29 3.583333 3.875 2.166667     19
## 119 119      M  31       39 4.083333 3.875 1.666667     30
## 120 120      F  20       36 4.250000 2.375 2.083333     22
## 121 121      F  22       29 3.416667 3.000 2.833333     16
## 122 122      F  22       21 3.083333 3.375 3.416667     16
## 123 123      M  21       31 3.500000 2.750 3.333333     19
## 124 124      M  22       40 3.666667 4.500 2.583333     30
## 125 125      F  21       31 4.250000 2.625 2.833333     23
## 126 126      F  21       23 4.250000 2.750 3.333333     19
## 127 127      F  21       28 3.833333 3.250 3.000000     18
## 128 128      F  21       37 4.416667 4.125 2.583333     28
## 129 129      F  20       26 3.500000 3.375 2.416667     21
## 130 130      F  21       24 3.583333 2.750 3.583333     19
## 131 131      F  25       30 3.666667 4.125 2.083333     27
## 132 132      M  21       28 2.083333 3.250 4.333333     24
## 133 133      F  24       29 4.250000 2.875 2.666667     21
## 134 134      F  20       24 3.583333 2.875 3.000000     20
## 135 135      M  21       31 4.000000 2.375 2.666667     28
## 136 136      F  20       19 3.333333 3.875 2.166667     12
## 137 137      F  20       20 3.500000 2.125 2.666667     21
## 138 138      F  18       38 3.166667 4.000 2.250000     28
## 139 139      F  21       34 3.583333 3.250 2.666667     31
## 140 140      F  19       37 3.416667 2.625 3.333333     18
## 141 141      F  21       29 4.250000 2.750 3.500000     25
## 142 142      F  20       23 3.250000 4.000 2.750000     19
## 143 143      M  21       41 4.416667 3.000 2.000000     21
## 144 144      F  20       27 3.250000 3.375 2.833333     16
## 145 145      F  21       35 3.916667 3.875 3.500000      7
## 146 146      F  20       34 3.583333 3.250 2.500000     21
## 147 147      F  18       32 4.500000 3.375 3.166667     17
## 148 148      M  22       33 3.583333 4.125 3.083333     22
## 149 149      F  22       33 3.666667 3.500 2.916667     18
## 150 150      M  24       35 2.583333 2.000 3.166667     25
## 151 151      F  19       32 4.166667 3.625 2.500000     24
## 152 152      F  20       31 3.250000 3.375 3.833333     23
## 153 153      F  20       28 4.333333 2.125 2.250000     23
## 154 154      F  17       17 3.916667 4.625 3.416667     26
## 155 155      M  19       19 2.666667 2.500 3.750000     12
## 156 156      F  20       35 3.083333 2.875 3.000000     32
## 157 157      F  20       24 3.750000 2.750 2.583333     22
## 158 158      F  20       21 4.166667 4.000 3.333333     20
## 159 159      F  20       29 4.166667 2.375 2.833333     21
## 160 160      F  19       19 3.250000 3.875 3.000000     23
## 161 161      F  19       20 4.083333 3.375 2.833333     20
## 162 162      F  22       42 2.916667 1.750 3.166667     28
## 163 163      M  35       41 3.833333 3.000 2.750000     31
## 164 164      F  18       37 3.166667 2.625 3.416667     18
## 165 165      F  19       36 3.416667 2.625 3.000000     30
## 166 166      M  21       18 4.083333 3.375 2.666667     19

let’s make it in “lrn2014_AGA”

lrn2014_AGA <- read.csv (file = "C:/Users/ahmed/Desktop/IODS-project/data/learning2014_AGA.csv")

str(lrn2014_AGA)
## 'data.frame':    166 obs. of  8 variables:
##  $ X       : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ gender  : Factor w/ 2 levels "F","M": 1 2 1 2 2 1 2 1 2 1 ...
##  $ Age     : int  53 55 49 53 49 38 50 37 37 42 ...
##  $ Attitude: int  37 31 25 35 37 38 35 29 38 21 ...
##  $ deep    : num  3.58 2.92 3.5 3.5 3.67 ...
##  $ stra    : num  3.38 2.75 3.62 3.12 3.62 ...
##  $ surf    : num  2.58 3.17 2.25 2.25 2.83 ...
##  $ Points  : int  25 12 24 10 22 21 21 31 24 26 ...
dim(lrn2014_AGA)
## [1] 166   8

structure shows that we have data frame of 166 observations about 8 variables describing students’ performance.

Graphical overview of the data

now let’s have a graphical overview of the data, can we access ggplot2 and GGally library? NO! we need to install package first!

library(ggplot2)

library(GGally)

plot <- ggpairs(lrn2014_AGA, mapping = aes(col = gender, alpha = 0.3), lower = list(combo = wrap("facethist", bins = 20)))

plot

looking onto our plots we can have an idea about normality of distribution, different variables correlation, Our sample included more females almost double males, We can see for example that Age is more correlated with strategic thinking, then with Attitude and deep thinking almost similarily, while it is not correlated Points and superficial thinking.The attitude is relatively highly correlated with the Points earned, however, it’s also correlated to deep thinking more than with strategic thinking. Deep thinking is somehow correlated with strategic thinking.Strategic thinking has somthing to do with Points Whereas superficial thinking is not correlated with Points.

summary(lrn2014_AGA)
##        X          gender       Age           Attitude          deep      
##  Min.   :  1.00   F:110   Min.   :17.00   Min.   :14.00   Min.   :1.583  
##  1st Qu.: 42.25   M: 56   1st Qu.:21.00   1st Qu.:26.00   1st Qu.:3.333  
##  Median : 83.50           Median :22.00   Median :32.00   Median :3.667  
##  Mean   : 83.50           Mean   :25.51   Mean   :31.43   Mean   :3.680  
##  3rd Qu.:124.75           3rd Qu.:27.00   3rd Qu.:37.00   3rd Qu.:4.083  
##  Max.   :166.00           Max.   :55.00   Max.   :50.00   Max.   :4.917  
##       stra            surf           Points     
##  Min.   :1.250   Min.   :1.583   Min.   : 7.00  
##  1st Qu.:2.625   1st Qu.:2.417   1st Qu.:19.00  
##  Median :3.188   Median :2.833   Median :23.00  
##  Mean   :3.121   Mean   :2.787   Mean   :22.72  
##  3rd Qu.:3.625   3rd Qu.:3.167   3rd Qu.:27.75  
##  Max.   :5.000   Max.   :4.333   Max.   :33.00

Regression Model fitting

Now let’s hypthesize a model to test how Attitude, deep and strategic thinking affect student’s exam points

fit <- lm(Points ~ Attitude + deep + stra, data = lrn2014_AGA) 

summary(fit)
## 
## Call:
## lm(formula = Points ~ Attitude + deep + stra, data = lrn2014_AGA)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -17.5239  -3.4276   0.5474   3.8220  11.5112 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 11.39145    3.40775   3.343  0.00103 ** 
## Attitude     0.35254    0.05683   6.203 4.44e-09 ***
## deep        -0.74920    0.75066  -0.998  0.31974    
## stra         0.96208    0.53668   1.793  0.07489 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.289 on 162 degrees of freedom
## Multiple R-squared:  0.2097, Adjusted R-squared:  0.195 
## F-statistic: 14.33 on 3 and 162 DF,  p-value: 2.521e-08

Summary showing in the coefficients section that there is higher probability that deep thinking values are wrong, so it should be rejected from our model.Now let’s return back to our fit model and try to refine by backwards elimination

fit <- lm(Points ~ Attitude + stra, data = lrn2014_AGA) 

summary(fit)
## 
## Call:
## lm(formula = Points ~ Attitude + stra, data = lrn2014_AGA)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -17.6436  -3.3113   0.5575   3.7928  10.9295 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  8.97290    2.39591   3.745  0.00025 ***
## Attitude     0.34658    0.05652   6.132 6.31e-09 ***
## stra         0.91365    0.53447   1.709  0.08927 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.289 on 163 degrees of freedom
## Multiple R-squared:  0.2048, Adjusted R-squared:  0.1951 
## F-statistic: 20.99 on 2 and 163 DF,  p-value: 7.734e-09

I am still not convinced to keep strategic thinking, let’s trim it!

fit <- lm(Points ~ Attitude , data = lrn2014_AGA) 

summary(fit)
## 
## Call:
## lm(formula = Points ~ Attitude, data = lrn2014_AGA)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.9763  -3.2119   0.4339   4.1534  10.6645 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 11.63715    1.83035   6.358 1.95e-09 ***
## Attitude     0.35255    0.05674   6.214 4.12e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.32 on 164 degrees of freedom
## Multiple R-squared:  0.1906, Adjusted R-squared:  0.1856 
## F-statistic: 38.61 on 1 and 164 DF,  p-value: 4.119e-09

According to this we can conclude that there is some statistical relationship between Student attitude and his exam points. what about the low R-squared? is it always bad? please see: http://blog.minitab.com/blog/adventures-in-statistics-2/regression-analysis-how-do-i-interpret-r-squared-and-assess-the-goodness-of-fit

Model Analysis

let’s have alook on the distribution and variability of the data around the regression line using some diagnostic plots

plot(fit, which = c(1, 2, 5))

The low R-squared graph shows that even noisy, high-variability data can have a significant trend.The trend indicates that the predictor variable still provides information about the response even though data points fall further from the regression line.

we assume that errors are normally distributed, right? well look at the QQ-plot you will find that most of the points fit to the underlying line (more or less), so our assumption of normal distribution for the errors is ok! next plot shows how the residuals are reasonably random spread around our model, which is good hopefully, as it tells that size of errors shold not depend on explanatory variables. Final plot; residuals vs. leverage, showing that although we have some outliers but they are more or less equally distributed exerting regular leverage, that I feel that we don’t need to worry about!


Logistic regression

Here we will practice some priciples of logistic regression using the joined student alcohol consumption data, let’s have a look on that

analys3 <-read.csv("C:/Users/ahmed/Desktop/IODS-project/data/joined data set for analysis.csv")

glimpse(analys3)
## Observations: 382
## Variables: 36
## $ X          <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
## $ ï..school  <fctr> GP, GP, GP, GP, GP, GP, GP, GP, GP, GP, GP, GP, GP...
## $ sex        <fctr> F, F, F, F, F, M, M, F, M, M, F, F, M, M, M, F, F,...
## $ age        <int> 18, 17, 15, 15, 16, 16, 16, 17, 15, 15, 15, 15, 15,...
## $ address    <fctr> U, U, U, U, U, U, U, U, U, U, U, U, U, U, U, U, U,...
## $ famsize    <fctr> GT3, GT3, LE3, GT3, GT3, LE3, LE3, GT3, LE3, GT3, ...
## $ Pstatus    <fctr> A, T, T, T, T, T, T, A, A, T, T, T, T, T, A, T, T,...
## $ Medu       <int> 4, 1, 1, 4, 3, 4, 2, 4, 3, 3, 4, 2, 4, 4, 2, 4, 4, ...
## $ Fedu       <int> 4, 1, 1, 2, 3, 3, 2, 4, 2, 4, 4, 1, 4, 3, 2, 4, 4, ...
## $ Mjob       <fctr> at_home, at_home, at_home, health, other, services...
## $ Fjob       <fctr> teacher, other, other, services, other, other, oth...
## $ reason     <fctr> course, course, other, home, home, reputation, hom...
## $ nursery    <fctr> yes, no, yes, yes, yes, yes, yes, yes, yes, yes, y...
## $ internet   <fctr> no, yes, yes, yes, no, yes, yes, no, yes, yes, yes...
## $ guardian   <fctr> mother, father, mother, mother, father, mother, mo...
## $ traveltime <int> 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, ...
## $ studytime  <int> 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 3, 1, 3, ...
## $ failures   <int> 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
## $ schoolsup  <fctr> yes, no, yes, no, no, no, no, yes, no, no, no, no,...
## $ famsup     <fctr> no, yes, no, yes, yes, yes, no, yes, yes, yes, yes...
## $ paid       <fctr> no, no, yes, yes, yes, yes, no, no, yes, yes, yes,...
## $ activities <fctr> no, no, no, yes, no, yes, no, no, no, yes, no, yes...
## $ higher     <fctr> yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, ...
## $ romantic   <fctr> no, no, no, yes, no, no, no, no, no, no, no, no, n...
## $ famrel     <int> 4, 5, 4, 3, 4, 5, 4, 4, 4, 5, 3, 5, 4, 5, 4, 4, 3, ...
## $ freetime   <int> 3, 3, 3, 2, 3, 4, 4, 1, 2, 5, 3, 2, 3, 4, 5, 4, 2, ...
## $ goout      <int> 4, 3, 2, 2, 2, 2, 4, 4, 2, 1, 3, 2, 3, 3, 2, 4, 3, ...
## $ Dalc       <int> 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
## $ Walc       <int> 1, 1, 3, 1, 2, 2, 1, 1, 1, 1, 2, 1, 3, 2, 1, 2, 2, ...
## $ health     <int> 3, 3, 3, 5, 5, 5, 3, 1, 1, 5, 2, 4, 5, 3, 3, 2, 2, ...
## $ absences   <int> 5, 3, 8, 1, 2, 8, 0, 4, 0, 0, 1, 2, 1, 1, 0, 5, 8, ...
## $ G1         <int> 2, 7, 10, 14, 8, 14, 12, 8, 16, 13, 12, 10, 13, 11,...
## $ G2         <int> 8, 8, 10, 14, 12, 14, 12, 9, 17, 14, 11, 12, 14, 11...
## $ G3         <int> 8, 8, 11, 14, 12, 14, 12, 10, 18, 14, 12, 12, 13, 1...
## $ alc_use    <dbl> 1.0, 1.0, 2.5, 1.0, 1.5, 1.5, 1.0, 1.0, 1.0, 1.0, 1...
## $ high_use   <lgl> FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FAL...

This data approach student achievement in secondary education of two Portuguese schools. The data (in the two sets) attributes include student grades, demographic, social and school related features and it was collected by using school reports and questionnaires, more details can be found here, I have performed some data wrangling to Keep only the students present in both data sets, combine the ‘duplicated’ answers in the joined data, take the average of the answers related to weekday and weekend alcohol consumption and create a new logical column ‘high_use’ which is TRUE for students for which ‘alc_use’ is greater than 2 (and FALSE otherwise), and the Rscript for that can be found here

The purpose

The purpose of analysis is to study the relationships between high/low alcohol consumption and some of the other variables in the data. To do this, we choose 4 interesting variables in the data; absences,quality of family relationship, sex (M) and free time after school. We hypthesize that those factors are correlated with higher alchol consumption.

Let’s have a look on that:

g1 <- ggplot(analys3, aes(x = high_use, y = absences, col = sex))

g1 + geom_boxplot()

g2 <- ggplot(analys3, aes(x = high_use, y = famrel, col = sex))

g2 + geom_boxplot()

g3 <- ggplot(analys3, aes(x = high_use, y = freetime, col = sex))

g3 + geom_boxplot()

analys3 %>% group_by(sex, absences, famrel, high_use) %>% summarise(count = n(), mean_freetime = mean(freetime))
## # A tibble: 149 x 6
## # Groups:   sex, absences, famrel [?]
##       sex absences famrel high_use count mean_freetime
##    <fctr>    <int>  <int>    <lgl> <int>         <dbl>
##  1      F        0      3    FALSE     2      2.500000
##  2      F        0      3     TRUE     3      3.333333
##  3      F        0      4    FALSE    15      2.933333
##  4      F        0      4     TRUE     2      3.500000
##  5      F        0      5    FALSE    11      2.636364
##  6      F        0      5     TRUE     1      4.000000
##  7      F        1      1    FALSE     1      2.000000
##  8      F        1      2    FALSE     1      3.000000
##  9      F        1      2     TRUE     1      3.000000
## 10      F        1      3    FALSE     6      3.000000
## # ... with 139 more rows

According to previous summaries; high_use is more related with higher absences espicially for males, weaker family relationship status equally for males and females and unlikely to be correlated with freetime espicially for males.

Fitting a model

To statistically test this lets fit logistic regression to explore the relationship between our chosen variables and the binary high/low alcohol consumption variable as the target variable.

m <- glm(high_use ~ absences + sex + famrel + freetime, data = analys3, family = "binomial")

summary(m)
## 
## Call:
## glm(formula = high_use ~ absences + sex + famrel + freetime, 
##     family = "binomial", data = analys3)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.9125  -0.8195  -0.5923   1.0419   2.0860  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -1.56113    0.62549  -2.496 0.012565 *  
## absences     0.09488    0.02244   4.229 2.35e-05 ***
## sexM         0.92271    0.24859   3.712 0.000206 ***
## famrel      -0.34855    0.13181  -2.644 0.008187 ** 
## freetime     0.33967    0.12673   2.680 0.007358 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 465.68  on 381  degrees of freedom
## Residual deviance: 417.44  on 377  degrees of freedom
## AIC: 427.44
## 
## Number of Fisher Scoring iterations: 4

so, in the summary of our model we can taste the close correlation between absences, sex variables and higher use of alchol, and less correlation yet present between status of family relatoiship and freetime with higher alchol consumption.

let’s print out the coefficients of the model to use to obtain Odds ratio (OR) and then confidence intervals (CI)

coef(m)
## (Intercept)    absences        sexM      famrel    freetime 
## -1.56112511  0.09487753  0.92270514 -0.34854597  0.33967147
OR <- coef(m) %>% exp()

CI <- confint(m) %>% exp()
## Waiting for profiling to be done...
cbind(OR, CI)
##                    OR     2.5 %    97.5 %
## (Intercept) 0.2098998 0.0600191 0.7022687
## absences    1.0995242 1.0542744 1.1516588
## sexM        2.5160876 1.5542543 4.1270709
## famrel      0.7057135 0.5433500 0.9127012
## freetime    1.4044861 1.0989755 1.8082673

Based on that we can see that family relation status is less likely to correlate with higher alchol consumption (contradicting our initial hypothesis) as it shows less than 1 OR with a CI crossing line at 1, followed by absences, then with more likelihood of correlation follws freetime (again challenging our initial hypothesis) and SexM variables. So, I would conclude that higher alchol consumption is much correlated with SexM and freetime.

Exploring the predictive power of our model

m <- glm(high_use ~ freetime + absences + sex, data = analys3, family = "binomial")

probabilities <- predict(m, type = "response")

analys3 <- mutate(analys3, probability = probabilities)

analys3 <- mutate(analys3, prediction = (probability > 0.5))

select(analys3, freetime, absences, sex, high_use, probability, prediction) %>% tail(10)
##     freetime absences sex high_use probability prediction
## 373        3        0   M    FALSE   0.2696155      FALSE
## 374        4        7   M     TRUE   0.4945212      FALSE
## 375        3        1   F    FALSE   0.1449414      FALSE
## 376        4        6   F    FALSE   0.2697703      FALSE
## 377        4        2   F    FALSE   0.1998871      FALSE
## 378        3        2   F    FALSE   0.1574882      FALSE
## 379        2        2   F    FALSE   0.1227034      FALSE
## 380        1        3   F    FALSE   0.1034644      FALSE
## 381        4        4   M     TRUE   0.4218155      FALSE
## 382        4        2   M     TRUE   0.3749754      FALSE
table(high_use = analys3$high_use, prediction = analys3$prediction) %>% prop.table() %>% addmargins()
##         prediction
## high_use      FALSE       TRUE        Sum
##    FALSE 0.66492147 0.03664921 0.70157068
##    TRUE  0.23036649 0.06806283 0.29842932
##    Sum   0.89528796 0.10471204 1.00000000
g <- ggplot(analys3, aes(x = probability, y = high_use, col = prediction)) 

g + geom_point()

It is evident that our prediction is not sensitive enough to predict higher alchol consumption; however, it was relatively specific in prdicting lower alchol consumers.

Now, let’s compute the total proportion of inaccurately classified individuals

loss_func <- function(class, prob) {
  n_wrong <- abs(class - prob) > 0.5
  mean(n_wrong)
}

loss_func(class = analys3$high_use, prob = analys3$probability)
## [1] 0.2670157

so, in our model the mean of incorrectly classified observations is around 0.267

Cross validation

Performing 10-fold cross-validation on our model, compute the average number of wrong predictions in the (training) data, compare to average number of wrong predictions in the cross validation

loss_func <- function(class, prob) {
  n_wrong <- abs(class - prob) > 0.5
  mean(n_wrong)
}

loss_func(class = analys3$high_use, prob = analys3$probability)
## [1] 0.2670157
library(boot)
cv <- cv.glm(data = analys3, cost = loss_func, glmfit = m, K = 10)

cv$delta[1]
## [1] 0.2748691

prediction error higher on the testing data compared to the training data.


Clustering and classification

Analysis exercises

We will work on the Boston data from the MASS package which comprises Housing Values in Suburbs of Boston, let’s load and explore it.

library(MASS)
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
## 
##     select
Ex4 <- Boston
str(Ex4)
## 'data.frame':    506 obs. of  14 variables:
##  $ crim   : num  0.00632 0.02731 0.02729 0.03237 0.06905 ...
##  $ zn     : num  18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
##  $ indus  : num  2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
##  $ chas   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ nox    : num  0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
##  $ rm     : num  6.58 6.42 7.18 7 7.15 ...
##  $ age    : num  65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
##  $ dis    : num  4.09 4.97 4.97 6.06 6.06 ...
##  $ rad    : int  1 2 2 3 3 3 5 5 5 5 ...
##  $ tax    : num  296 242 242 222 222 222 311 311 311 311 ...
##  $ ptratio: num  15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
##  $ black  : num  397 397 393 395 397 ...
##  $ lstat  : num  4.98 9.14 4.03 2.94 5.33 ...
##  $ medv   : num  24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...

Our data frame(Boston) has 506 obseravations of 14 variables which are all numerical except for two integers (Charles River dummy variable (= 1 if tract bounds river; 0 otherwise and index of accessibility to radial highways).

It is nice to have some graphical overview of the data as follows:

summary(Ex4)
##       crim                zn             indus            chas        
##  Min.   : 0.00632   Min.   :  0.00   Min.   : 0.46   Min.   :0.00000  
##  1st Qu.: 0.08204   1st Qu.:  0.00   1st Qu.: 5.19   1st Qu.:0.00000  
##  Median : 0.25651   Median :  0.00   Median : 9.69   Median :0.00000  
##  Mean   : 3.61352   Mean   : 11.36   Mean   :11.14   Mean   :0.06917  
##  3rd Qu.: 3.67708   3rd Qu.: 12.50   3rd Qu.:18.10   3rd Qu.:0.00000  
##  Max.   :88.97620   Max.   :100.00   Max.   :27.74   Max.   :1.00000  
##       nox               rm             age              dis        
##  Min.   :0.3850   Min.   :3.561   Min.   :  2.90   Min.   : 1.130  
##  1st Qu.:0.4490   1st Qu.:5.886   1st Qu.: 45.02   1st Qu.: 2.100  
##  Median :0.5380   Median :6.208   Median : 77.50   Median : 3.207  
##  Mean   :0.5547   Mean   :6.285   Mean   : 68.57   Mean   : 3.795  
##  3rd Qu.:0.6240   3rd Qu.:6.623   3rd Qu.: 94.08   3rd Qu.: 5.188  
##  Max.   :0.8710   Max.   :8.780   Max.   :100.00   Max.   :12.127  
##       rad              tax           ptratio          black       
##  Min.   : 1.000   Min.   :187.0   Min.   :12.60   Min.   :  0.32  
##  1st Qu.: 4.000   1st Qu.:279.0   1st Qu.:17.40   1st Qu.:375.38  
##  Median : 5.000   Median :330.0   Median :19.05   Median :391.44  
##  Mean   : 9.549   Mean   :408.2   Mean   :18.46   Mean   :356.67  
##  3rd Qu.:24.000   3rd Qu.:666.0   3rd Qu.:20.20   3rd Qu.:396.23  
##  Max.   :24.000   Max.   :711.0   Max.   :22.00   Max.   :396.90  
##      lstat            medv      
##  Min.   : 1.73   Min.   : 5.00  
##  1st Qu.: 6.95   1st Qu.:17.02  
##  Median :11.36   Median :21.20  
##  Mean   :12.65   Mean   :22.53  
##  3rd Qu.:16.95   3rd Qu.:25.00  
##  Max.   :37.97   Max.   :50.00
library(ggplot2)
library(GGally)
plot1 <- ggpairs(Ex4,       
  upper = list(continuous = wrap("cor", size = 3)), 
  lower = list(continuous = wrap("points", alpha = .2, size = .6),
               combo = wrap("facethist", bins = 10))) +
  theme(
    axis.text.x = element_text(angle = 90, color = "black", size = 7, vjust = .5),
    axis.text.y = element_text(color = "black", size = 7))
  
  
plot1

Can we have better visualization for the correlation? I think corrplot() function (from the corrplot package) could help, let’s see!

library(corrplot)
## corrplot 0.84 loaded
library(tidyverse)
## -- Attaching packages -------------------------------------------------------------------------- tidyverse 1.2.1 --
## v tibble  1.3.4     v purrr   0.2.4
## v tidyr   0.7.2     v stringr 1.2.0
## v readr   1.1.1     v forcats 0.2.0
## -- Conflicts ----------------------------------------------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
## x MASS::select()  masks dplyr::select()
cor_matrix<-cor(Ex4) %>% round(2)
cor_matrix
##          crim    zn indus  chas   nox    rm   age   dis   rad   tax
## crim     1.00 -0.20  0.41 -0.06  0.42 -0.22  0.35 -0.38  0.63  0.58
## zn      -0.20  1.00 -0.53 -0.04 -0.52  0.31 -0.57  0.66 -0.31 -0.31
## indus    0.41 -0.53  1.00  0.06  0.76 -0.39  0.64 -0.71  0.60  0.72
## chas    -0.06 -0.04  0.06  1.00  0.09  0.09  0.09 -0.10 -0.01 -0.04
## nox      0.42 -0.52  0.76  0.09  1.00 -0.30  0.73 -0.77  0.61  0.67
## rm      -0.22  0.31 -0.39  0.09 -0.30  1.00 -0.24  0.21 -0.21 -0.29
## age      0.35 -0.57  0.64  0.09  0.73 -0.24  1.00 -0.75  0.46  0.51
## dis     -0.38  0.66 -0.71 -0.10 -0.77  0.21 -0.75  1.00 -0.49 -0.53
## rad      0.63 -0.31  0.60 -0.01  0.61 -0.21  0.46 -0.49  1.00  0.91
## tax      0.58 -0.31  0.72 -0.04  0.67 -0.29  0.51 -0.53  0.91  1.00
## ptratio  0.29 -0.39  0.38 -0.12  0.19 -0.36  0.26 -0.23  0.46  0.46
## black   -0.39  0.18 -0.36  0.05 -0.38  0.13 -0.27  0.29 -0.44 -0.44
## lstat    0.46 -0.41  0.60 -0.05  0.59 -0.61  0.60 -0.50  0.49  0.54
## medv    -0.39  0.36 -0.48  0.18 -0.43  0.70 -0.38  0.25 -0.38 -0.47
##         ptratio black lstat  medv
## crim       0.29 -0.39  0.46 -0.39
## zn        -0.39  0.18 -0.41  0.36
## indus      0.38 -0.36  0.60 -0.48
## chas      -0.12  0.05 -0.05  0.18
## nox        0.19 -0.38  0.59 -0.43
## rm        -0.36  0.13 -0.61  0.70
## age        0.26 -0.27  0.60 -0.38
## dis       -0.23  0.29 -0.50  0.25
## rad        0.46 -0.44  0.49 -0.38
## tax        0.46 -0.44  0.54 -0.47
## ptratio    1.00 -0.18  0.37 -0.51
## black     -0.18  1.00 -0.37  0.33
## lstat      0.37 -0.37  1.00 -0.74
## medv      -0.51  0.33 -0.74  1.00
corrplot(cor_matrix, method="circle", type = "upper", cl.pos = "b", tl.pos = "d", tl.cex = 0.6)

So, now we can rather easily interpret or taste the correlation pattern between many variables. We can say for example that crim shows relatively more correlation with rad and proportion of non-retail business acres per town is highly correlated with nitrogen oxides concentration (parts per 10 million). Same for correlation between rad and tax and the negative correlation between age and dis. However, the current data state is a bit diverse and unscaled that hinders true interpretations; which should be dealt with next.

Ex4_scaled <- scale(Ex4)
summary(Ex4_scaled)
##       crim                 zn               indus        
##  Min.   :-0.419367   Min.   :-0.48724   Min.   :-1.5563  
##  1st Qu.:-0.410563   1st Qu.:-0.48724   1st Qu.:-0.8668  
##  Median :-0.390280   Median :-0.48724   Median :-0.2109  
##  Mean   : 0.000000   Mean   : 0.00000   Mean   : 0.0000  
##  3rd Qu.: 0.007389   3rd Qu.: 0.04872   3rd Qu.: 1.0150  
##  Max.   : 9.924110   Max.   : 3.80047   Max.   : 2.4202  
##       chas              nox                rm               age         
##  Min.   :-0.2723   Min.   :-1.4644   Min.   :-3.8764   Min.   :-2.3331  
##  1st Qu.:-0.2723   1st Qu.:-0.9121   1st Qu.:-0.5681   1st Qu.:-0.8366  
##  Median :-0.2723   Median :-0.1441   Median :-0.1084   Median : 0.3171  
##  Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
##  3rd Qu.:-0.2723   3rd Qu.: 0.5981   3rd Qu.: 0.4823   3rd Qu.: 0.9059  
##  Max.   : 3.6648   Max.   : 2.7296   Max.   : 3.5515   Max.   : 1.1164  
##       dis               rad               tax             ptratio       
##  Min.   :-1.2658   Min.   :-0.9819   Min.   :-1.3127   Min.   :-2.7047  
##  1st Qu.:-0.8049   1st Qu.:-0.6373   1st Qu.:-0.7668   1st Qu.:-0.4876  
##  Median :-0.2790   Median :-0.5225   Median :-0.4642   Median : 0.2746  
##  Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
##  3rd Qu.: 0.6617   3rd Qu.: 1.6596   3rd Qu.: 1.5294   3rd Qu.: 0.8058  
##  Max.   : 3.9566   Max.   : 1.6596   Max.   : 1.7964   Max.   : 1.6372  
##      black             lstat              medv        
##  Min.   :-3.9033   Min.   :-1.5296   Min.   :-1.9063  
##  1st Qu.: 0.2049   1st Qu.:-0.7986   1st Qu.:-0.5989  
##  Median : 0.3808   Median :-0.1811   Median :-0.1449  
##  Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
##  3rd Qu.: 0.4332   3rd Qu.: 0.6024   3rd Qu.: 0.2683  
##  Max.   : 0.4406   Max.   : 3.5453   Max.   : 2.9865
Ex4_scaled <- as.data.frame(Ex4_scaled)
class(Ex4_scaled)
## [1] "data.frame"

In the scaled data we can notice that all the means are set to 0.0000. Now, let’s focus on the crime rate varable and try to categorize.

summary(Ex4_scaled$crim)
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## -0.419367 -0.410563 -0.390280  0.000000  0.007389  9.924110
bins <- quantile(Ex4_scaled$crim)
bins
##           0%          25%          50%          75%         100% 
## -0.419366929 -0.410563278 -0.390280295  0.007389247  9.924109610
crime <- cut(Ex4_scaled$crim, breaks = bins, include.lowest = TRUE, label = c("low", "med_low", "med_high", "high"))

table(crime)
## crime
##      low  med_low med_high     high 
##      127      126      126      127
Ex4_scalednocrim <- dplyr::select(Ex4_scaled, -crim)

Ex4_scaledw <- data.frame(Ex4_scalednocrim, crime)

summary(Ex4_scaledw)
##        zn               indus              chas              nox         
##  Min.   :-0.48724   Min.   :-1.5563   Min.   :-0.2723   Min.   :-1.4644  
##  1st Qu.:-0.48724   1st Qu.:-0.8668   1st Qu.:-0.2723   1st Qu.:-0.9121  
##  Median :-0.48724   Median :-0.2109   Median :-0.2723   Median :-0.1441  
##  Mean   : 0.00000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
##  3rd Qu.: 0.04872   3rd Qu.: 1.0150   3rd Qu.:-0.2723   3rd Qu.: 0.5981  
##  Max.   : 3.80047   Max.   : 2.4202   Max.   : 3.6648   Max.   : 2.7296  
##        rm               age               dis               rad         
##  Min.   :-3.8764   Min.   :-2.3331   Min.   :-1.2658   Min.   :-0.9819  
##  1st Qu.:-0.5681   1st Qu.:-0.8366   1st Qu.:-0.8049   1st Qu.:-0.6373  
##  Median :-0.1084   Median : 0.3171   Median :-0.2790   Median :-0.5225  
##  Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
##  3rd Qu.: 0.4823   3rd Qu.: 0.9059   3rd Qu.: 0.6617   3rd Qu.: 1.6596  
##  Max.   : 3.5515   Max.   : 1.1164   Max.   : 3.9566   Max.   : 1.6596  
##       tax             ptratio            black             lstat        
##  Min.   :-1.3127   Min.   :-2.7047   Min.   :-3.9033   Min.   :-1.5296  
##  1st Qu.:-0.7668   1st Qu.:-0.4876   1st Qu.: 0.2049   1st Qu.:-0.7986  
##  Median :-0.4642   Median : 0.2746   Median : 0.3808   Median :-0.1811  
##  Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
##  3rd Qu.: 1.5294   3rd Qu.: 0.8058   3rd Qu.: 0.4332   3rd Qu.: 0.6024  
##  Max.   : 1.7964   Max.   : 1.6372   Max.   : 0.4406   Max.   : 3.5453  
##       medv              crime    
##  Min.   :-1.9063   low     :127  
##  1st Qu.:-0.5989   med_low :126  
##  Median :-0.1449   med_high:126  
##  Mean   : 0.0000   high    :127  
##  3rd Qu.: 0.2683                 
##  Max.   : 2.9865
boston_scaled <- Ex4_scaledw

Now, we need to divide the dataset to train and test sets, so that 80% of the data belongs to the train set.

n <- nrow(boston_scaled)
n
## [1] 506
# choose randomly 80% of the rows
train_set <- sample(n,  size = n * 0.8)

train <- boston_scaled[train_set,]
 
test <- boston_scaled[-train_set,]

Now, let’s fit the linear discriminant analysis on the train set. Use the categorical crime rate as the target variable and all the other variables in the dataset as predictor variables.

lda.fit <- lda(crime ~ ., data = train)

lda.fit
## Call:
## lda(crime ~ ., data = train)
## 
## Prior probabilities of groups:
##       low   med_low  med_high      high 
## 0.2326733 0.2623762 0.2524752 0.2524752 
## 
## Group means:
##                   zn      indus        chas        nox          rm
## low       0.89144221 -0.8729270 -0.14667693 -0.8684264  0.46519641
## med_low  -0.05927783 -0.3133379 -0.08661679 -0.5845279 -0.09605925
## med_high -0.37710480  0.2000248  0.30665626  0.3973176  0.19698470
## high     -0.48724019  1.0171096 -0.04073494  1.0081713 -0.42413844
##                 age        dis        rad        tax     ptratio
## low      -0.9053466  0.8094302 -0.6739843 -0.7690895 -0.38338225
## med_low  -0.3561053  0.3896918 -0.5463205 -0.5051313 -0.05789749
## med_high  0.3934475 -0.4020899 -0.3873706 -0.2973215 -0.41555376
## high      0.7948847 -0.8446033  1.6382099  1.5141140  0.78087177
##                black       lstat        medv
## low       0.39220600 -0.80656991  0.56957823
## med_low   0.32414486 -0.15199725  0.02966739
## med_high  0.05326296 -0.08100412  0.23713107
## high     -0.83374439  0.88606252 -0.68238258
## 
## Coefficients of linear discriminants:
##                 LD1          LD2          LD3
## zn       0.03711715  0.724599086 -0.953578705
## indus    0.03208902 -0.209561223  0.177101519
## chas    -0.07894705 -0.117799740  0.003897276
## nox      0.34409749 -0.686213290 -1.165768627
## rm      -0.10008290 -0.136616480 -0.168365469
## age      0.25379228 -0.310644127  0.035889321
## dis     -0.10612899 -0.177194337  0.322101487
## rad      3.01551254  0.838620019 -0.248590181
## tax     -0.01889099 -0.029666674  0.583153776
## ptratio  0.06038409  0.170634649 -0.182661456
## black   -0.11998338  0.005993161  0.127508387
## lstat    0.19623326 -0.139906976  0.442573499
## medv     0.16688460 -0.263384241 -0.117461745
## 
## Proportion of trace:
##    LD1    LD2    LD3 
## 0.9446 0.0419 0.0135
str(train)
## 'data.frame':    404 obs. of  14 variables:
##  $ zn     : num  -0.487 -0.487 3.372 -0.487 -0.487 ...
##  $ indus  : num  -0.755 1.015 -1.077 1.015 1.015 ...
##  $ chas   : num  -0.272 -0.272 -0.272 -0.272 -0.272 ...
##  $ nox    : num  -0.481 0.365 -1.387 0.218 1.366 ...
##  $ rm     : num  -0.631 -1.608 1.664 0.217 0.188 ...
##  $ age    : num  -0.255 1.116 -1.221 0.228 1.056 ...
##  $ dis    : num  -0.198 -1.047 1.207 -0.427 -0.765 ...
##  $ rad    : num  -0.522 1.66 -0.752 1.66 1.66 ...
##  $ tax    : num  -0.767 1.529 -0.974 1.529 1.529 ...
##  $ ptratio: num  0.344 0.806 -1.18 0.806 0.806 ...
##  $ black  : num  0.229 -1.596 0.325 0.402 -0.575 ...
##  $ lstat  : num  -0.174 1.04 -1.336 0.239 0.932 ...
##  $ medv   : num  -0.2754 -0.6777 2.3341 0.0725 -1.0365 ...
##  $ crime  : Factor w/ 4 levels "low","med_low",..: 2 4 1 3 4 3 4 2 2 1 ...
# the function for lda biplot arrows
lda.arrows <- function(x, myscale = 1, arrow_heads = 0.1, color = "red", tex = 0.75, choices = c(1,2)){
  heads <- coef(x)
  arrows(x0 = 0, y0 = 0, 
         x1 = myscale * heads[,choices[1]], 
         y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads)
  text(myscale * heads[,choices], labels = row.names(heads), 
       cex = tex, col=color, pos=3)
}

# classes as numeric
classes <- as.numeric(train$crime)

# plot results
plot(lda.fit, dimen = 2, col = classes, pch = classes)
lda.arrows(lda.fit, myscale = 1)

Save the crime categories from the test set and then remove the categorical crime variable from the test dataset. Then predict the classes with the LDA model on the test data.

cross tabulate the results

table(correct = correct_classes, predicted = lda.pred$class) %>% addmargins()
##           predicted
## correct    low med_low med_high high Sum
##   low       17      14        2    0  33
##   med_low    2      16        2    0  20
##   med_high   0      11       13    0  24
##   high       0       0        0   25  25
##   Sum       19      41       17   25 102

Out of this eventual table we can say that if we use our model to predict low crime rate based on other variables we are 6X more likely to have correct prediction, 1.78X likely to predict med_low crime rate, almost around 13X likely to predict med_high and high crime rates. Thus it is relatively less reliable in detecting med_low crime rate.

We will now reload the Boston dataset and standardize the dataset then calculate the distances between the observations.

library(MASS)
data('Boston')

Boston_scaled <- scale(Boston) %>% as.data.frame()
class(Boston_scaled)
## [1] "data.frame"
# euclidean distance matrix
dist_eu <- dist(Boston_scaled)
dist_eu
##              1          2          3          4          5          6
## 2    1.9356773                                                       
## 3    2.2809294  2.0310282                                            
## 4    2.5741175  2.3335157  1.1821904                                 
## 5    2.6906020  2.3727561  1.0547043  0.5825442                      
## 6    2.2407228  1.5500088  1.6132814  1.1071450  1.3164896           
## 7    1.7841939  1.7596710  2.8618599  3.1442855  3.1914074  2.4808284
## 8    2.7044618  2.3009840  3.3564325  3.8007319  3.6212338  3.1606647
## 9    4.2499491  3.6273509  5.1392781  5.4228501  5.2929937  4.6304102
## 10   2.6004186  2.1461113  3.5717921  3.8424245  3.8066037  3.0860989
## 11   2.9830212  2.4522334  3.9081075  4.2460387  4.1584319  3.5556295
## 12   2.1627378  1.8431989  3.2621150  3.5423466  3.5620670  2.7855722
## 13   2.3474898  2.3961628  3.3166430  3.4200903  3.5255881  2.8556346
## 14   3.1042847  1.9073015  2.9412306  2.8551660  3.0241470  2.1271805
## 15   3.2129096  1.8101805  3.1496767  3.2490143  3.3086129  2.4705351
## 16   3.1719345  2.0479070  3.0855291  2.9710555  3.1648969  2.2435735
## 17   3.3095910  2.5650444  2.9988025  2.7105117  3.0036105  2.2790853
## 18   3.4318000  2.0207180  3.4693674  3.5705115  3.5905279  2.7701408
## 19   3.7973987  2.9622022  3.8503720  3.6901047  3.8977688  3.0553380
## 20   3.3255715  2.0972980  3.4242734  3.4452857  3.5636989  2.6395599
## 21   4.2659710  2.9325392  4.5891698  4.7403393  4.7104165  3.8594717
## 22   3.4105035  2.0039904  3.4015256  3.5637858  3.5547817  2.7627571
## 23   3.7788405  2.3778856  3.8884911  4.0706930  4.0220356  3.3022630
## 24   4.0634446  2.6680259  4.2921561  4.4625961  4.4139266  3.6111587
## 25   3.6962449  2.2513336  3.8348011  3.9729878  3.9590156  3.1303024
## 26   3.9665447  2.6598721  4.2214341  4.2775733  4.3247407  3.4086222
## 27   3.6082433  2.1624096  3.7229891  3.8136376  3.8293109  2.9441365
## 28   3.8252920  2.4642364  3.9305380  4.0552749  4.0473891  3.2753819
## 29   3.3285595  1.8813755  3.1381429  3.3590215  3.3116939  2.6876276
## 30   3.1824604  1.8199041  2.7875057  3.0366750  2.9760505  2.4831042
## 31   4.3258853  2.9767731  4.6129108  4.7408021  4.7022799  3.8879968
## 32   3.5818372  2.1638212  3.7143634  3.8936730  3.9016428  3.0804523
## 33   4.9292496  3.7818419  5.1173768  5.2445190  5.1780153  4.5465022
## 34   4.0204095  2.6768335  4.3224722  4.4673378  4.4670051  3.6005772
## 35   4.3294564  3.1040739  4.4925960  4.6891291  4.6425136  3.9617999
## 36   2.4830279  1.4069001  2.8423008  2.9331795  3.0720937  2.1066812
## 37   2.5936826  1.5786261  2.9253572  2.9761888  3.1092033  2.1605166
## 38   2.5740245  1.8307468  2.7704509  2.6169500  2.8714297  1.9172281
## 39   2.7012337  2.1232577  2.6624006  2.4757165  2.7064331  1.9700399
## 40   3.4993032  4.0708979  3.7116599  3.4290812  3.5905877  3.5251675
## 41   3.7922666  4.4494881  3.6967326  3.4303495  3.5661148  3.7791546
## 42   2.9924747  2.8965812  2.3661617  1.9250102  2.3171665  2.2085503
## 43   2.9336977  2.7031301  2.6715097  2.2212323  2.6226032  2.0907834
## 44   2.9369495  2.6562502  2.6971419  2.2684547  2.6358500  2.1149131
## 45   2.3900661  1.5337953  2.4531803  2.2495278  2.5048668  1.5467280
## 46   2.6778910  1.9529768  3.0211046  2.8124352  3.0900845  2.0698176
## 47   2.8102260  2.0048566  3.0920622  2.9313810  3.1247354  2.2248512
## 48   3.0622541  1.6315542  3.4313880  3.5794491  3.5384777  2.6905181
## 49   4.7028207  3.5373350  5.2068233  5.3295644  5.2252596  4.4436889
## 50   2.9721026  1.7575811  3.3295887  3.2663100  3.3451233  2.3278008
## 51   2.4936650  2.0446192  3.1116661  2.9280944  3.0759166  2.2277925
## 52   2.0791770  1.5757458  2.6901255  2.6009107  2.7419825  1.8404145
## 53   2.4146263  2.5727104  2.4579929  2.0521225  2.3882542  1.9947573
## 54   2.5859830  2.5574530  2.9481602  2.5631132  2.8593832  2.1653881
## 55   4.6298697  4.3273594  5.0065158  4.6969228  4.7832378  4.2434683
## 56   4.7273967  5.2266740  4.6017672  4.2256293  4.2710824  4.5269676
## 57   4.1777550  4.6190924  4.6906479  4.2862251  4.4278606  4.1584462
## 58   4.4155816  5.2393243  4.9483590  4.7685487  4.8297108  4.8402925
## 59   3.2860769  2.7922716  3.0908851  2.4572342  2.7472672  2.0903479
## 60   3.0400145  2.2882291  3.1782618  2.7452331  2.9691975  2.0395071
## 61   3.2936427  2.2936753  3.5525063  3.2625584  3.3653647  2.4022463
## 62   3.4010859  2.2309917  3.7337030  3.6559422  3.6608558  2.7762440
## 63   2.8163903  1.9954249  2.6136013  2.3001474  2.4239784  1.7236933
## 64   3.1744072  2.5630626  2.6573790  2.1547315  2.2618960  1.9713783
## 65   3.3794731  2.9493848  2.4668275  1.9332947  1.8085327  2.0643819
## 66   3.6474387  4.3829307  4.4171371  4.1564671  4.3736307  4.0657821
## 67   3.7171177  4.2199602  4.7591759  4.5452751  4.7204783  4.1679546
## 68   3.0846224  2.5656744  3.0776642  2.5953711  2.9221392  2.1101866
## 69   3.2624645  2.4344454  3.5794328  3.2446058  3.4657866  2.4767091
## 70   2.9228067  2.2447243  2.9845109  2.5729165  2.8601352  1.9472170
## 71   3.3837268  2.8244155  2.7501295  2.4689994  2.8067441  2.4291816
## 72   3.3468094  2.5317886  3.0492621  2.8226578  3.1090739  2.4100112
## 73   3.4200337  2.8424595  3.0015060  2.6877540  3.0649907  2.4762976
## 74   3.4319400  2.8342911  2.9221943  2.6342922  2.9687076  2.4897769
## 75   3.3805936  2.9966710  3.0064268  2.9497567  3.2523030  2.8599157
## 76   2.8076761  1.8679317  2.5529415  2.7543275  2.9343858  2.3088156
## 77   2.8722314  1.5606839  2.8004811  3.2184726  3.2519981  2.5883797
## 78   2.8793393  1.9209278  2.7680645  2.9818854  3.1464489  2.4676521
## 79   2.9183146  1.7377377  2.7115576  2.9328498  3.0276882  2.3693539
## 80   3.0514789  2.2051206  3.0288643  3.0941544  3.3280237  2.5512020
## 81   2.4705154  2.3264404  1.9484758  1.5572024  1.8233472  1.6181814
## 82   2.1758072  1.4669939  2.0454744  2.0279384  2.0943464  1.4928276
## 83   2.4879027  2.2053208  2.4046786  2.0003479  2.2941306  1.6662684
## 84   2.3475598  1.8337030  2.4681063  2.1785857  2.4160054  1.5672472
## 85   2.1404592  1.2537716  1.9471894  1.7947334  1.9705159  1.1505053
## 86   1.9687823  1.2366414  1.3808707  1.3976350  1.5528745  0.9598901
## 87   2.4543334  1.5531738  2.5964093  2.4587331  2.6046038  1.7139497
## 88   2.1012124  1.1992518  2.2739958  2.2682829  2.4507657  1.5034576
## 89   1.7940213  1.3973066  1.8020147  2.2974059  2.2717561  1.9720900
## 90   1.7507417  1.7046585  1.1811112  1.6594158  1.6519599  1.6836477
## 91   1.6613999  1.1654026  2.1307367  2.3705038  2.4586685  1.7674920
## 92   1.6736984  1.0897368  2.1958877  2.4795758  2.5518788  1.8328241
## 93   2.5359377  2.0340048  2.5415804  2.9902080  3.1075033  2.6461629
## 94   2.8258088  2.6150966  2.7796490  3.0099654  3.2374862  2.7929480
## 95   2.6788980  1.8536127  2.9362867  3.4539913  3.4903804  2.8815572
## 96   1.8571534  1.5646920  1.5331783  1.7088325  1.7981470  1.4164769
## 97   2.0381368  1.1377793  2.5096289  2.6351695  2.7002620  1.8416765
## 98   3.1850158  3.2245464  1.7340743  2.3598281  2.0371746  2.9583649
## 99   3.4256551  3.6849796  1.8684545  2.1178107  1.9416391  2.9986215
## 100  2.3196220  2.2490727  1.0874949  1.6260237  1.4436884  1.9941256
## 101  3.1407596  2.1921548  2.5009947  2.9059868  2.8297902  2.5892183
## 102  3.0523336  2.1878778  2.3754011  2.7196557  2.7090688  2.4708045
## 103  4.8326550  4.1505539  4.7542712  4.9709743  5.0003479  4.5731192
## 104  3.4245306  2.2237036  3.4500245  3.7264200  3.7165097  3.0453972
## 105  3.4069762  2.2575377  3.4067959  3.7196672  3.7068922  3.0652959
## 106  3.8281565  2.6701490  3.9919246  4.3008813  4.2546827  3.5605182
## 107  3.9161580  2.7512398  4.0799927  4.3649994  4.3084325  3.6276623
## 108  3.4928302  2.3828330  3.5143624  3.8208442  3.8010249  3.1779315
## 109  3.4350778  2.2853511  3.3443649  3.7285992  3.6736671  3.1480383
## 110  3.5642726  2.3613488  3.5788946  3.8970394  3.8437431  3.2382086
## 111  3.2829443  2.3142131  3.1334793  3.2551461  3.3271424  2.7382381
## 112  2.3555199  1.8769599  2.5866643  3.2327741  3.1978701  2.8353248
## 113  3.0830887  2.3458384  3.7565519  4.2422321  4.2088781  3.5196749
## 114  3.0893744  2.3109930  3.7036389  4.2156273  4.1534986  3.5219851
## 115  2.5594785  2.0057712  3.1808777  3.7040886  3.7390044  3.1078168
## 116  3.0456435  2.3338747  3.7167076  4.1786882  4.1680507  3.4668351
## 117  2.4605952  1.8944872  2.9810245  3.4486117  3.4810479  2.8621146
## 118  2.5326913  1.9148506  3.1889751  3.6474199  3.7017146  2.9748462
## 119  2.9188742  2.3141309  3.5330291  3.9430605  3.9640747  3.2764866
## 120  2.7827289  2.2084938  3.4821891  3.8089537  3.8904870  3.1095755
## 121  4.4029357  3.4139841  4.2413621  4.8562654  4.8767944  4.3760794
## 122  4.4306321  3.3807236  4.3000802  4.9719911  4.9661325  4.4660390
## 123  4.6824844  3.5848608  4.5948957  5.2789535  5.2241687  4.7331920
## 124  5.2891453  4.1650569  5.3480280  5.9774262  5.8860480  5.3728732
## 125  4.7354829  3.6320023  4.7217640  5.3917761  5.3505604  4.8131369
## 126  4.4920686  3.4456804  4.3540447  5.0492433  5.0228265  4.5401878
## 127  5.5499021  4.4443398  5.7053200  6.2902971  6.2127633  5.6434520
## 128  5.0151817  3.9565382  5.1070635  5.6134835  5.6016136  4.9919002
## 129  4.7672318  3.7387788  4.6189100  5.2340243  5.1772497  4.7718777
## 130  5.1034678  4.0231762  5.2490412  5.7256325  5.7206537  5.0785141
## 131  4.6139318  3.5994372  4.3931852  5.0152108  4.9725144  4.5791416
## 132  4.5858332  3.5600483  4.3797832  4.9809568  4.9489539  4.5206704
## 133  4.5212885  3.5305628  4.1889816  4.8218647  4.7737840  4.4106886
## 134  4.7739135  3.6879786  4.7418552  5.2563219  5.2430202  4.6679271
## 135  5.1920385  4.1402506  5.2500365  5.7358638  5.7250078  5.1267912
## 136  4.8107227  3.7399587  4.6791911  5.2709994  5.2067465  4.7779650
## 137  4.8704377  3.8091768  4.8591525  5.3921053  5.3665261  4.8264412
## 138  4.7399163  3.7164010  4.6036964  5.2132144  5.1688671  4.7529175
## 139  5.2793628  4.1963117  5.4179383  5.9278103  5.8877062  5.3068433
## 140  4.9593704  3.9049056  4.9099470  5.4879388  5.4258396  4.9580982
## 141  5.3547173  4.2855543  5.4103271  5.9406788  5.8663069  5.3869305
## 142  6.6079306  5.5528070  6.8949806  7.3119504  7.2218157  6.5923332
## 143  6.9463969  6.8317165  7.8089373  8.3212805  8.2751369  7.7901410
## 144  5.6200410  5.4953902  6.5987638  7.2015968  7.1378579  6.6132672
## 145  6.1674025  5.9764380  7.2432254  7.7659028  7.7309011  7.0904979
## 146  6.0792984  5.9712756  6.8968717  7.5156317  7.4353651  7.0377521
## 147  5.5230898  5.5472924  6.4374877  7.0364005  7.0386134  6.5263498
## 148  6.0881274  5.9082764  7.1178963  7.6477169  7.6007346  6.9902733
## 149  5.8053455  5.6678210  6.7618947  7.3278643  7.2653315  6.7225877
## 150  5.1916765  5.1555832  6.1901446  6.8031424  6.7752509  6.2476077
## 151  4.5593474  4.7083083  5.3895160  6.1090882  6.0703544  5.7039894
## 152  4.8551482  4.9445080  5.8364563  6.4677432  6.4773388  5.9299363
## 153  6.3742190  6.4509580  7.2805310  7.7344415  7.7993411  7.2296832
## 154  4.9961689  5.0641703  5.8938659  6.5420279  6.5261584  6.0519308
## 155  6.1263021  6.2038531  6.8435460  7.4112127  7.3965134  7.0428551
## 156  6.9132994  7.0117658  7.5514224  8.0418178  8.0591736  7.7240380
## 157  6.0783486  6.0871870  7.0105876  7.5195864  7.5613748  6.9828639
## 158  3.7869175  4.0086275  3.5161353  4.5722413  4.4183748  4.5882165
## 159  3.3951139  3.3764767  4.0188357  4.8732662  4.8782900  4.4427647
## 160  4.3487259  4.6453381  5.0465499  5.8171366  5.7957322  5.5366866
## 161  5.1323778  5.1840638  5.4484556  6.0964233  6.0973634  5.8481773
## 162  4.4472763  4.7956901  3.7482087  4.7795552  4.5778835  5.0679986
## 163  6.0874349  6.3370184  5.5339694  6.3174234  6.1359941  6.5737789
## 164  6.3233723  6.5814845  5.6653035  6.4536191  6.2453811  6.8035055
## 165  3.3895736  3.2109173  4.1143880  4.8862945  4.8806677  4.3598084
## 166  3.6954711  3.6157197  4.2131394  5.0059422  4.9932905  4.5956958
## 167  4.6900326  4.9953147  3.9082140  4.9659246  4.7128309  5.3067466
## 168  3.7821411  3.6817096  4.3739904  5.0730633  5.0898201  4.6247617
## 169  3.4914483  3.3808713  4.0320910  4.8924322  4.8518244  4.4895753
## 170  3.3685457  3.2380085  3.9440732  4.8094438  4.7712289  4.4033175
## 171  3.7768534  3.4992525  4.5852079  5.3004572  5.3022864  4.7258893
## 172  3.5363112  3.3011397  4.3393208  5.0943340  5.0982617  4.5303984
## 173  2.5248736  2.0790903  3.4863302  3.8149909  3.7984380  2.9862575
## 174  1.6085836  1.4643271  2.4243650  2.9148473  2.9071359  2.3460043
## 175  1.7969874  1.6716072  2.8262061  3.0915936  3.1917095  2.3707045
## 176  1.7749345  2.3008650  1.9465474  2.0780615  2.2896660  2.0639247
## 177  1.7066694  1.7151264  2.5649321  2.6567361  2.8217387  2.0532685
## 178  1.2978846  1.3372028  2.1195509  2.4906109  2.5763602  1.9189842
## 179  1.5367932  1.7685775  1.6342305  2.2854410  2.2135839  2.1110463
## 180  2.3132847  2.4448335  1.3406629  1.7571413  1.6495258  2.0241626
## 181  3.0522984  3.0565280  1.8841321  2.5745160  2.2027482  2.9492128
## 182  2.3628993  2.2071251  2.1548619  2.3914313  2.3300707  2.0438719
## 183  2.6200332  2.5607151  1.7580535  2.4280751  2.1638891  2.5108585
## 184  2.2183365  1.9031859  1.9970943  2.5046472  2.3708140  2.1290434
## 185  2.6740114  1.9229193  3.2122673  3.4283070  3.3810844  2.5646408
## 186  2.1813847  1.6049935  2.3222762  2.5205040  2.4522083  1.8849835
## 187  3.7531166  4.0105970  2.2289672  2.6277375  2.3101266  3.3917099
## 188  2.0883658  3.2055943  2.8049856  3.0219370  3.0731065  3.0862970
## 189  2.1973350  3.3060535  2.9880167  3.0033183  3.1737964  3.0375377
## 190  2.4067450  3.4787481  2.6821211  2.8855877  2.8929476  3.1868829
## 191  2.9552832  3.8611245  3.0357083  2.9350625  3.0109656  3.2755354
## 192  2.4596499  3.3865397  2.9652674  2.8579555  3.0020406  2.9677315
## 193  2.9241983  3.8769764  2.9330321  2.8705020  2.9485731  3.2945121
## 194  3.2069244  4.0551846  3.5393115  3.3015876  3.4752828  3.5210435
## 195  2.9676933  3.8118072  3.4772888  3.2524531  3.4478393  3.3419268
## 196  4.6825805  5.7297365  4.5068371  4.5843915  4.4741076  5.1528497
## 197  3.9556646  5.1166692  4.5797452  4.5898260  4.6236345  4.8193294
## 198  3.8616334  4.9332698  4.6471353  4.6656534  4.6832306  4.7634285
## 199  3.9557599  5.0682413  4.5619696  4.6050980  4.5951743  4.8080607
##              7          8          9         10         11         12
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8    1.5095700                                                       
## 9    2.8745287  2.0581191                                            
## 10   1.1561304  1.0821813  1.9716672                                 
## 11   1.8379764  1.3751490  1.7254583  0.8879389                      
## 12   0.7991461  1.3281029  2.4873440  0.5845270  1.2785903           
## 13   1.1071829  2.2169980  3.0344240  1.7969167  2.3441110  1.6767558
## 14   2.8486373  3.5054113  4.4011938  3.2571412  3.6149378  3.0177002
## 15   2.9278040  3.2710047  4.0566979  3.0771850  3.2795024  2.9046098
## 16   2.8912887  3.6101758  4.4397342  3.3342128  3.7103776  3.0946661
## 17   3.1953155  4.1262775  5.0765999  3.8632833  4.3074314  3.5937555
## 18   2.9368276  3.1575921  3.6757917  2.9816085  3.1176053  2.9070925
## 19   3.3802027  4.1357527  4.6521104  3.8311657  4.2421904  3.6910328
## 20   2.9439039  3.4633501  4.0897504  3.2292869  3.5166705  3.0507081
## 21   3.5177223  3.4011731  3.2196693  3.2382495  3.2204558  3.3292244
## 22   2.9766296  3.1173134  3.7470312  3.0394253  3.1960924  2.9454896
## 23   3.2224328  3.1769403  3.4089372  3.0592456  2.9927608  3.0871810
## 24   3.3764594  3.2324404  3.2396777  3.1019641  3.0562698  3.1721548
## 25   3.1142168  3.1456454  3.4661806  2.9714035  3.0184994  2.9555518
## 26   3.2996035  3.4716399  3.5776610  3.1619587  3.3011580  3.1796282
## 27   3.0140633  3.1441211  3.5524505  2.9318962  3.0773530  2.8880483
## 28   3.2553846  3.3087765  3.5431539  3.0858286  3.1075201  3.1236487
## 29   3.0779270  3.1487403  3.9299983  3.0781426  3.1017524  2.9783742
## 30   3.0664505  3.2022829  4.1519715  3.1993170  3.2550891  3.0715541
## 31   3.5285890  3.3839943  3.1053030  3.1860077  3.1120833  3.3262455
## 32   3.2013217  3.3049138  3.7920368  3.1073158  3.1487193  3.0199875
## 33   4.1544224  3.9614117  3.4910275  3.8089097  3.6695942  4.0453009
## 34   3.3790833  3.3939156  3.4051534  3.1771565  3.1899284  3.2103309
## 35   3.7821396  3.6717705  3.6596206  3.5143116  3.4234829  3.6240624
## 36   2.3035559  3.0043172  3.8878187  2.7774948  3.0965457  2.5002532
## 37   2.2776451  2.9851109  3.7895780  2.7679799  3.1180170  2.5414517
## 38   2.3688392  3.3620203  4.2837226  3.0685050  3.5154064  2.7766761
## 39   2.5183681  3.4771445  4.4555458  3.2915669  3.7414771  3.0396196
## 40   3.9827942  4.7413561  5.9667253  4.6591368  5.0590897  4.4061158
## 41   4.4484656  5.1754133  6.5515228  5.1726460  5.5504561  4.9047917
## 42   3.1865370  4.2769761  5.5377467  4.0326195  4.4585891  3.7386640
## 43   2.8467378  4.0287158  5.1487889  3.7023233  4.2319541  3.4078866
## 44   2.7804147  3.9324373  5.0024344  3.6067364  4.1066365  3.3363433
## 45   1.9147166  2.9648263  3.9909599  2.5649952  3.0572151  2.2994956
## 46   2.1060808  3.2239136  4.0054996  2.7644508  3.2840020  2.5080142
## 47   2.0658597  3.0145784  3.6715908  2.6166101  3.0642187  2.4658791
## 48   2.0689894  2.0162617  2.3697544  1.6936010  1.7555771  1.8161277
## 49   3.4439873  2.8887706  1.6692419  2.7327211  2.5808153  3.1318461
## 50   1.8474807  2.3581540  2.8622063  1.9225700  2.3860358  1.9031400
## 51   1.5972150  2.4992468  3.3197716  1.9573318  2.4697434  1.8264455
## 52   1.4615982  2.3292312  3.5012981  1.8404158  2.3797786  1.5555646
## 53   2.4546912  3.5810258  4.8813443  3.2438096  3.7476134  2.9324259
## 54   2.1792785  3.3446040  4.3965952  2.9131681  3.4951825  2.6550317
## 55   4.2790627  4.6418918  5.0339762  4.3520753  4.5918508  4.3294175
## 56   5.0702280  5.5432756  6.7847294  5.5118953  5.8310897  5.3563796
## 57   4.2579745  4.8381501  5.7934495  4.5485780  4.9260934  4.3982021
## 58   4.7164791  5.1799547  6.3584793  5.0954362  5.4378019  4.9233982
## 59   2.9744816  3.8546262  4.8796570  3.4653799  3.9582025  3.2514533
## 60   2.5557573  3.3529654  4.2051163  2.9071026  3.3615417  2.7108616
## 61   2.5059801  2.9493550  3.5546566  2.5144186  2.9128688  2.4516523
## 62   2.6895538  2.7361035  3.2262332  2.3705750  2.5348814  2.3827958
## 63   2.6375228  3.1838066  4.3841583  2.9077245  3.2660071  2.6780624
## 64   2.9406599  3.5079161  4.6672348  3.2783400  3.6047300  3.1332963
## 65   3.4251932  3.6523343  5.0938224  3.6739995  3.9944690  3.5603029
## 66   3.8464752  4.7252604  5.7248599  4.4170364  4.8327843  4.1762872
## 67   3.5185386  4.2647010  4.9007864  3.8759221  4.2704290  3.7284751
## 68   2.6867837  3.7437454  4.6585422  3.3205600  3.8493324  3.0807671
## 69   2.4632881  3.3231502  3.8333544  2.7871087  3.2528425  2.6652068
## 70   2.4477594  3.4419648  4.3438249  3.0008116  3.5137484  2.7676043
## 71   3.2226377  4.2774898  5.3372500  3.9910713  4.4143759  3.7275183
## 72   2.8403728  3.8575426  4.6886854  3.4979052  3.9515847  3.2839351
## 73   3.1846121  4.3180025  5.3127497  3.9645721  4.4498225  3.6745048
## 74   3.1718163  4.2400981  5.2183482  3.9214164  4.3625045  3.6719300
## 75   3.1711167  4.2753217  5.3100505  4.0136286  4.4441263  3.7261576
## 76   2.3517797  3.2402380  4.2928208  2.9819180  3.3462868  2.7122645
## 77   2.2696537  2.7111239  3.6530573  2.5645160  2.7755947  2.3809931
## 78   2.3394206  3.2025972  4.1447447  2.9478022  3.3042588  2.6992267
## 79   2.1618605  2.8393600  3.7784982  2.5954247  2.9199776  2.4197030
## 80   2.4449904  3.4499088  4.3242374  3.1030397  3.5489456  2.8338636
## 81   2.8376425  3.7061200  5.0913724  3.5905177  3.9929483  3.2903789
## 82   2.3738609  2.9222585  4.2754750  2.8159804  3.1196971  2.5375474
## 83   2.5831389  3.5593406  4.7466158  3.3162046  3.7730449  3.0241611
## 84   2.3135756  3.2154591  4.3515956  2.9374731  3.3902357  2.6502059
## 85   2.1209268  2.9489121  4.1446213  2.7800808  3.1572508  2.5156112
## 86   2.3478096  3.0916670  4.5255646  3.0539198  3.4137114  2.7337001
## 87   2.0851720  2.8898798  3.7868177  2.6727736  3.0687528  2.4818640
## 88   2.1619054  3.0086352  4.1218187  2.8281875  3.2160380  2.5153849
## 89   2.6260207  3.0324499  4.5168914  3.1046266  3.2396774  2.7700224
## 90   2.6584777  3.2388983  4.8244404  3.3749126  3.6158435  3.0460007
## 91   2.0945825  2.8035637  4.0410548  2.7454194  3.0260569  2.4259167
## 92   2.1299212  2.7669859  4.0167406  2.7137167  2.9765083  2.3824961
## 93   2.3557721  3.1585846  4.3528831  3.0324965  3.3489699  2.7273785
## 94   2.6998340  3.7429971  4.9063076  3.5622845  4.0037780  3.2332512
## 95   2.2440438  2.7238620  3.7600399  2.6241977  2.8557832  2.3799897
## 96   2.4732586  3.1632084  4.6121769  3.2189607  3.5712550  2.9099946
## 97   2.0456506  2.6349401  3.6642317  2.5279938  2.8146020  2.2841931
## 98   4.1272933  4.2708675  6.0167538  4.6843898  4.7941448  4.4381021
## 99   4.3028188  4.7387943  6.4650530  5.0904194  5.3588343  4.8256219
## 100  3.1792615  3.5730086  5.2166656  3.8432337  4.0393718  3.5681975
## 101  3.2941250  3.5358787  4.7445986  3.7205390  3.8773957  3.5102712
## 102  3.3001367  3.7005401  4.9388736  3.8071107  3.9914793  3.5574500
## 103  4.7899018  5.0070434  5.5481919  4.8918997  4.9957297  4.8396341
## 104  3.1616199  3.3521502  4.0158272  3.3345592  3.4282104  3.2034156
## 105  3.2364642  3.4304749  4.1690827  3.4473826  3.5506359  3.2916898
## 106  3.4294433  3.4327514  3.8418244  3.4883022  3.5482898  3.4267965
## 107  3.4229848  3.3927272  3.6841066  3.4512552  3.4898685  3.4339504
## 108  3.2684664  3.4525529  4.1023523  3.4870431  3.5797501  3.3618565
## 109  3.3681995  3.4573525  4.2573616  3.5215238  3.5337293  3.3743365
## 110  3.2659355  3.3210765  3.9011162  3.3619238  3.3814114  3.2816183
## 111  3.0731275  3.6016387  4.3698169  3.5289369  3.7398396  3.3602791
## 112  2.3781569  2.7344413  3.9950182  2.8340914  2.9433203  2.5724135
## 113  2.4670540  2.5389428  3.0850356  2.5591622  2.6370353  2.4684653
## 114  2.4771324  2.4365730  2.9952918  2.4951775  2.4901586  2.4382077
## 115  2.3828255  2.8339617  3.7796914  2.7629863  2.9042947  2.4978669
## 116  2.4367370  2.6081219  3.1444682  2.5509458  2.6615420  2.4674584
## 117  2.0827518  2.6155674  3.6093979  2.5719746  2.8049916  2.3321687
## 118  2.1803379  2.6943227  3.6391072  2.5803193  2.8240815  2.3022115
## 119  2.2944175  2.6801791  3.3120389  2.6110940  2.8380226  2.4989436
## 120  2.1235990  2.7595923  3.4281602  2.5774810  2.8892548  2.3803677
## 121  3.7073122  4.0056589  4.5631225  4.0009817  4.1837520  3.8857431
## 122  3.7769015  3.9517570  4.4873821  3.9613905  4.0677311  3.8591711
## 123  3.9293948  3.8985834  4.2483609  3.9797631  4.0119140  3.9543868
## 124  4.3656315  4.1175361  3.9443547  4.1989167  4.0837137  4.3106770
## 125  3.9816960  3.9654459  4.2539353  4.0064833  4.0311001  3.9755735
## 126  3.8425851  3.9484578  4.4839956  4.0123287  4.1092689  3.9194222
## 127  4.5687890  4.3287731  3.9526769  4.3679782  4.2574198  4.5054311
## 128  4.3525144  4.3950006  4.5645233  4.3681099  4.3959576  4.3259139
## 129  4.3301582  4.3272220  4.8016704  4.3900479  4.3290161  4.3167013
## 130  4.3820294  4.4222592  4.4723801  4.3507542  4.3557567  4.3297798
## 131  4.2445498  4.3044999  4.9371715  4.3603405  4.3532946  4.2438288
## 132  4.1794922  4.2634224  4.8973677  4.3069628  4.3368219  4.1847049
## 133  4.1673165  4.2411927  5.0198023  4.3499120  4.4262907  4.2129064
## 134  4.1369026  4.2045851  4.5718284  4.1907583  4.2650993  4.1212609
## 135  4.5193554  4.5326747  4.6504140  4.4530871  4.4828958  4.4617548
## 136  4.2772476  4.2308985  4.6222137  4.2919798  4.2291202  4.2509582
## 137  4.2524448  4.2906595  4.5691846  4.2898654  4.3024987  4.2464070
## 138  4.3277146  4.3603976  4.8478918  4.3942655  4.3337387  4.3081755
## 139  4.5637190  4.4888364  4.4204399  4.4594321  4.3603833  4.4870728
## 140  4.3790799  4.3168437  4.5849267  4.3839004  4.3232628  4.3608015
## 141  4.6468080  4.4994577  4.3981900  4.5221764  4.3457551  4.5916347
## 142  5.5729025  5.2216898  4.4234339  5.2746461  5.1501321  5.4789006
## 143  6.2849604  6.1301278  5.8037140  6.1338791  6.0527372  6.2173981
## 144  4.8056177  4.5825177  4.2379605  4.6322197  4.5425375  4.7374671
## 145  5.2320412  5.0442409  4.3622263  4.9975132  4.9315242  5.1356044
## 146  5.4273349  5.1786682  4.8627631  5.1904238  5.0085585  5.3541549
## 147  5.0096916  5.0526506  5.1388477  4.9724307  5.0275193  4.9811148
## 148  5.1369601  4.9234795  4.2985824  4.9243804  4.8837804  5.0694716
## 149  4.8995136  4.6722989  4.2284875  4.7313480  4.7058442  4.8713906
## 150  4.4872316  4.4342661  4.3465280  4.4155018  4.3930654  4.4521903
## 151  4.1728044  4.2108180  4.7720070  4.3128932  4.3669189  4.2180955
## 152  4.3299208  4.4441749  4.7944717  4.4383258  4.6009517  4.3443692
## 153  5.9304996  6.1685041  6.3215586  6.0410885  6.2102915  5.9506990
## 154  4.4780103  4.5106177  4.7910878  4.5189999  4.6073467  4.4896055
## 155  5.8016330  5.8516115  6.1332300  5.8418979  5.8439550  5.7974310
## 156  6.6286420  6.7631139  6.9577843  6.6668748  6.7026812  6.6621935
## 157  5.5371856  5.6691223  5.6278748  5.4910161  5.5982242  5.5096901
## 158  3.9246244  3.9597815  5.6093553  4.4819557  4.7362232  4.2308222
## 159  3.1105945  3.3992699  4.5096597  3.5066170  3.7551095  3.2289090
## 160  4.2800300  4.4442654  5.3735591  4.5498626  4.6478761  4.3522414
## 161  5.0245709  5.2470772  6.1498479  5.3486562  5.5396882  5.1557186
## 162  4.8074552  4.8369295  6.6221844  5.4279026  5.6827420  5.1741941
## 163  6.4015692  6.3594650  7.8400047  6.8516075  7.0076476  6.6564128
## 164  6.6888874  6.6153765  8.0921498  7.1147072  7.1998974  6.9405241
## 165  2.6813645  2.9105945  3.7850223  2.9789192  3.2179770  2.7817790
## 166  3.2485003  3.4511916  4.3898064  3.5315280  3.7691662  3.3796786
## 167  5.0681457  4.9750809  6.7282320  5.6017793  5.7608840  5.3892176
## 168  3.1513077  3.4564592  4.1986271  3.4472954  3.7239775  3.3372132
## 169  3.0504736  3.1758229  4.1471636  3.3073811  3.4495871  3.1514792
## 170  2.9075147  3.0494596  4.0255957  3.1536873  3.2565146  2.9849239
## 171  3.0029512  3.1466522  3.6076367  3.0553403  3.1647176  2.9815923
## 172  2.8364694  3.0292133  3.7219248  2.9943144  3.1575196  2.8353916
## 173  2.0293374  2.2264354  3.0058073  2.3153262  2.6446758  2.1645481
## 174  1.9752471  2.4396862  3.7987896  2.5380520  2.7729403  2.2087917
## 175  1.7573578  2.5648857  3.6708289  2.4749562  2.8947195  2.1358747
## 176  2.4191602  3.4545390  4.9174949  3.4457838  3.8843581  3.0749859
## 177  1.5898393  2.6797369  3.8135171  2.4881865  2.9573033  2.1616489
## 178  1.7861830  2.5710988  4.0431447  2.5563202  2.9477940  2.1424503
## 179  2.3078958  2.7746116  4.4378780  3.0337125  3.2986082  2.7007802
## 180  3.1851524  3.6626310  5.3362091  3.9865391  4.3163150  3.6809384
## 181  3.8989966  3.8990313  5.5969838  4.4254177  4.5286865  4.2167644
## 182  2.7010503  3.1308062  4.5706756  3.4692896  3.9063491  3.2191385
## 183  3.4792107  3.5715854  5.3043828  4.0461759  4.2675047  3.7727164
## 184  2.8828933  3.0620123  4.6590057  3.4150319  3.7049120  3.1158557
## 185  2.3863086  2.4916156  3.3812592  2.6687219  3.0214228  2.5353653
## 186  2.1817455  2.5164266  3.7540944  2.7457380  3.0989561  2.5705711
## 187  4.5930607  4.7950241  6.5871058  5.3143400  5.5768155  5.0821518
## 188  2.7470780  3.4855271  4.9884247  3.5895530  3.9628790  3.2903887
## 189  2.7537151  3.7241299  5.1477072  3.6459824  4.1092283  3.3144377
## 190  3.1371539  3.7763677  5.3976718  3.9313309  4.2698178  3.6468310
## 191  3.3429318  4.0717382  5.6213318  4.1169658  4.5736432  3.8710668
## 192  2.8159373  3.6780594  5.1542383  3.5678908  4.0323156  3.2786094
## 193  3.4832746  4.2042632  5.8284165  4.2497020  4.6694522  3.9700336
## 194  3.6599803  4.5173314  5.8150625  4.3976567  4.8163145  4.1471065
## 195  3.4018398  4.2921814  5.5719637  4.1195723  4.5672839  3.8528510
## 196  5.4367967  5.7439911  7.3610170  6.0739917  6.3723548  5.8730198
## 197  4.4541724  4.9570130  6.3013360  4.9500608  5.2492765  4.7501410
## 198  4.1557499  4.5880705  5.7440432  4.5389191  4.8020970  4.4124494
## 199  4.3687651  4.7662419  6.0846069  4.8158329  5.0958174  4.6559723
##             13         14         15         16         17         18
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14   3.0658834                                                       
## 15   3.3405234  0.9367744                                            
## 16   3.0273470  0.2758607  1.1202682                                 
## 17   3.0812139  1.2244857  2.1108514  1.0757216                      
## 18   3.2210395  1.2110406  0.6594929  1.3021093  2.2670798           
## 19   3.1757532  1.7634207  2.2152181  1.5714186  1.5506513  2.1446790
## 20   3.1422967  0.7760617  0.8333488  0.7344435  1.7201299  0.7805656
## 21   3.7543230  2.4361579  1.8494246  2.4581713  3.3946342  1.3154506
## 22   3.3590267  1.2945799  0.6330267  1.4155829  2.4007106  0.3948462
## 23   3.5098177  1.9478842  1.2929166  2.0356418  2.9500481  0.7681670
## 24   3.6855687  2.2417421  1.5809335  2.3076665  3.2749855  1.0670601
## 25   3.4687378  1.6971508  0.9985836  1.7955823  2.7977743  0.5559626
## 26   3.5057440  1.9663902  1.4803126  1.9753820  2.8308425  1.1795657
## 27   3.3631827  1.4570015  0.8081145  1.5522362  2.5642662  0.4681726
## 28   3.5170471  1.9760560  1.3353867  2.0483006  2.8862558  1.0363280
## 29   3.5549193  1.5559369  0.7622008  1.7606632  2.6467553  0.8984443
## 30   3.5100756  1.4985741  0.9221360  1.7111243  2.4487243  1.1312965
## 31   3.7063159  2.5256616  1.9543666  2.5518855  3.4368612  1.3933969
## 32   3.6636673  1.6887085  0.8028575  1.8250284  2.8418720  0.7827940
## 33   4.1241813  3.4509351  2.9971942  3.4485379  4.0415490  2.5354553
## 34   3.6462415  2.1239708  1.4854382  2.1559574  3.1090615  1.0161662
## 35   4.0161425  2.8085107  2.1570952  2.8611079  3.6128024  1.8704692
## 36   2.5956534  1.2158608  1.2884726  1.2149789  1.8896180  1.3767497
## 37   2.4259026  1.2704413  1.4440919  1.2134752  1.7724882  1.4088364
## 38   2.3121493  1.2784969  1.9078408  1.1501970  1.1797285  1.9737485
## 39   2.2954021  1.6326126  2.3046013  1.5099638  1.1567134  2.3152134
## 40   3.9392379  4.2486582  4.6645126  4.2559818  3.9308291  4.8232053
## 41   4.4336113  4.6769290  5.1054210  4.7035406  4.2883681  5.3089880
## 42   2.8977089  3.0935551  3.7403357  3.0715021  2.3951258  3.9145116
## 43   2.4780495  2.7374517  3.4507410  2.6651818  2.0177826  3.5809097
## 44   2.3597336  2.7124404  3.4114324  2.6396977  2.0252307  3.5015236
## 45   1.8411603  1.9500547  2.4249249  1.9326322  1.9072676  2.5028584
## 46   1.8369088  2.0376685  2.5741840  1.9331701  1.8921835  2.5662104
## 47   1.6542187  2.1657056  2.6189083  2.0719375  2.0731978  2.4877462
## 48   2.4159628  2.4869198  2.1734135  2.5642044  3.2645166  1.9307652
## 49   3.4917212  3.9528167  3.5997698  3.9680759  4.6715888  3.1075571
## 50   1.8861665  2.1944608  2.3165836  2.1875955  2.6520748  2.1323246
## 51   1.4616671  2.7291765  3.0041162  2.7317997  2.8663567  2.9656312
## 52   1.8816201  2.5832088  2.7419013  2.6517204  2.9238854  2.8613113
## 53   2.3180172  3.1211934  3.6501090  3.1325306  2.7657673  3.8280270
## 54   1.8470525  2.9595513  3.5069078  2.9240370  2.6404197  3.5832149
## 55   4.2214922  3.9416093  4.1185283  3.9456938  4.0800968  4.0634488
## 56   5.0917371  5.6107683  5.9463628  5.6753855  5.3829708  6.1188737
## 57   4.2985044  4.9753868  5.2710954  5.0176747  4.9120190  5.4122009
## 58   4.8502044  5.9166021  6.1557419  5.9756798  5.8435154  6.3227036
## 59   2.8926584  2.4923936  3.0692903  2.5059904  2.2481262  3.2328579
## 60   2.5985724  1.9710988  2.3962575  1.9869505  2.1250002  2.4991957
## 61   2.6856640  2.1256306  2.2510899  2.1754675  2.6525442  2.2272907
## 62   3.1448464  2.3997598  2.0639207  2.5210690  3.2708264  2.0406405
## 63   3.0470505  2.1339504  2.2974489  2.2841693  2.5693507  2.5798532
## 64   3.0309986  2.6337283  2.9805330  2.7381415  2.6592574  3.1398616
## 65   3.7464012  3.6559394  3.8528945  3.8110798  3.7878109  4.0721357
## 66   3.7187246  4.7677200  5.1556388  4.7563732  4.5157672  5.2777769
## 67   3.3551001  4.5844450  4.8737987  4.5561278  4.5132369  4.8862000
## 68   2.4098931  2.3318883  2.9939615  2.2647202  1.9182814  3.0755725
## 69   2.1946056  2.2234242  2.6699355  2.1478615  2.2485881  2.5826643
## 70   2.2962518  2.0974585  2.6735845  2.0568324  1.9261270  2.7548945
## 71   2.8942229  2.5716798  3.2717963  2.5054706  1.8155474  3.3927253
## 72   2.4708739  2.1637126  2.8309645  2.0545569  1.6072512  2.8503097
## 73   2.8573613  2.4522021  3.2086861  2.3504758  1.6739270  3.3364188
## 74   2.7931610  2.5153754  3.2266158  2.4263665  1.7479338  3.3159307
## 75   2.8081119  2.6568665  3.3452747  2.5596543  1.9036959  3.4358900
## 76   2.3932076  1.8175092  2.2053372  1.8150430  1.8380632  2.3200960
## 77   2.6336406  1.8766502  1.7311068  1.9538055  2.4979941  1.7743444
## 78   2.3342066  1.8000659  2.1622774  1.7658503  1.8625020  2.2031467
## 79   2.2439954  1.8106215  2.0407377  1.8383201  2.0873888  2.0427850
## 80   2.3125679  1.8710507  2.4020540  1.7824609  1.7249212  2.4467013
## 81   2.8957432  2.5287892  3.0225366  2.5757213  2.2378359  3.2503046
## 82   2.8493868  2.1144538  2.1890889  2.2558917  2.5476990  2.4567543
## 83   2.5354733  2.2216492  2.7795044  2.2159162  1.9278673  2.9431994
## 84   2.4265884  1.9431499  2.3725896  1.9622897  1.9740498  2.5401758
## 85   2.2291489  1.7792363  2.1576309  1.8163360  1.8540564  2.2732080
## 86   2.6681363  1.9655322  2.2520461  2.0593963  2.0961795  2.5099097
## 87   1.9887876  1.7879013  2.1692171  1.7436291  1.8646139  2.1028550
## 88   2.3821266  1.6398723  1.9279501  1.6453882  1.8965272  2.0639662
## 89   3.2859195  2.5715026  2.3868271  2.7292435  3.1114459  2.7069901
## 90   3.0831831  2.6178532  2.7330010  2.7331647  2.7762316  3.0029364
## 91   2.4720602  2.0163575  2.0716007  2.0700625  2.3839567  2.2168799
## 92   2.6193311  2.0422541  1.9947500  2.1183369  2.5355509  2.1783941
## 93   2.5571579  2.3415207  2.5595854  2.3686332  2.4647957  2.6949052
## 94   2.5989812  2.5824300  3.0916111  2.5297997  2.2277568  3.2195150
## 95   2.6836479  2.3340841  2.2283329  2.3982008  2.8775667  2.3010924
## 96   2.7904695  2.3466029  2.5419074  2.4136488  2.4283842  2.7706635
## 97   2.3844751  1.9854649  1.9750839  2.0230801  2.4722417  2.0048852
## 98   4.6201177  4.1485917  4.1409676  4.3127739  4.2955539  4.4318481
## 99   4.4944527  4.2838829  4.5802746  4.3779339  3.9994443  4.8259726
## 100  3.5695951  3.1548716  3.2574559  3.2827209  3.2452848  3.5065037
## 101  3.7066260  1.8322984  1.6704656  1.9823950  2.4139829  1.8937334
## 102  3.6617117  1.7296252  1.7270187  1.8666827  2.1719706  2.0082124
## 103  5.0245312  3.8962907  3.5515866  3.9314864  4.2360095  3.6702309
## 104  3.5155180  1.6092910  1.0929518  1.6887161  2.5342841  0.9763982
## 105  3.6307863  1.6918023  1.1785728  1.7785593  2.5989637  1.1663883
## 106  3.7702553  2.1609120  1.6172328  2.2006036  3.0624350  1.3196472
## 107  3.6815892  2.2272065  1.7425882  2.2482514  3.0712172  1.3229909
## 108  3.5773845  1.7872809  1.3580437  1.8362953  2.5975904  1.2024136
## 109  3.8344751  1.9680058  1.3457322  2.1002355  2.8961901  1.4024529
## 110  3.6137215  1.9015314  1.3250659  1.9845140  2.8060287  1.0986841
## 111  3.1086516  1.3225284  1.5402846  1.2783647  1.6433518  1.4305905
## 112  2.9023120  2.3714000  2.1578115  2.4783874  2.9281760  2.2896774
## 113  2.8867177  2.5718980  2.1808952  2.6044565  3.3269320  1.9841241
## 114  2.9227180  2.6365304  2.1905018  2.6920583  3.4214936  1.9833778
## 115  2.8650550  2.2786849  2.0074289  2.3315832  2.9269740  2.0706232
## 116  2.8022129  2.5232595  2.1418661  2.5440618  3.2136160  1.9752291
## 117  2.4322106  2.0715531  1.9829764  2.0993326  2.5865090  1.9696852
## 118  2.6697324  2.0960346  1.8939621  2.1365432  2.7620940  1.9510981
## 119  2.4903803  2.3589634  2.1908892  2.3386940  2.8478472  2.0241062
## 120  2.2584331  2.1017015  2.1249103  2.0481281  2.5327362  1.9805444
## 121  3.8300071  3.1925567  3.1568451  3.1737576  3.5203284  3.0554323
## 122  4.0258328  3.2841141  3.0854511  3.3003505  3.7740064  3.0085644
## 123  4.1837800  3.5529777  3.2545991  3.5763371  4.1254780  3.0865750
## 124  4.5040332  4.1528365  3.7738486  4.1597196  4.7577980  3.4369867
## 125  4.2512735  3.5864178  3.2633034  3.6062597  4.1919539  3.0970693
## 126  4.1181321  3.3770285  3.1504321  3.3988113  3.8956975  3.0615471
## 127  4.6450653  4.3724237  4.0056379  4.3575454  4.9555178  3.6269837
## 128  4.5897963  3.2371512  2.8788778  3.2394036  3.9171025  2.6712046
## 129  4.6609663  3.2134381  2.7914020  3.2805370  3.9040800  2.7039566
## 130  4.5846435  3.2932949  2.9349392  3.2870243  3.9774434  2.6842343
## 131  4.6278251  3.0549893  2.6616761  3.1381593  3.7446084  2.6739104
## 132  4.5589601  2.9580960  2.5924843  3.0348622  3.6461863  2.6065627
## 133  4.5773036  2.9515083  2.6212077  3.0408886  3.6011044  2.6914869
## 134  4.4303588  2.9518553  2.6125275  2.9811221  3.6480801  2.4903450
## 135  4.7520749  3.4976196  3.0599952  3.5092221  4.1324324  2.9124046
## 136  4.5817460  3.1958874  2.7707380  3.2576620  3.8976666  2.6289181
## 137  4.4964722  3.1220078  2.7567147  3.1421705  3.7825225  2.5777351
## 138  4.6650627  3.1838423  2.7605169  3.2521615  3.8758417  2.6978345
## 139  4.7502416  3.5901167  3.1600091  3.5957980  4.2882601  2.8540930
## 140  4.6411970  3.3319088  2.9186442  3.3695221  4.0157872  2.7134748
## 141  4.7764483  3.7635189  3.3356993  3.7774834  4.4081754  2.9853137
## 142  5.5537410  5.0022528  4.6410790  4.9580434  5.6026314  4.1318812
## 143  6.3577362  6.9143938  6.6803554  6.8983408  7.3301298  6.4500820
## 144  4.9157558  5.6130769  5.3330915  5.5993778  6.1045127  5.0553945
## 145  5.2469097  5.9878839  5.7291118  5.9442101  6.4684827  5.3962534
## 146  5.5094864  6.1850401  5.8041144  6.1894005  6.6133777  5.5846123
## 147  5.2183474  5.6650182  5.3655152  5.6598301  6.0580037  5.2959747
## 148  5.1436650  5.9250224  5.6832304  5.8828331  6.3844754  5.3494283
## 149  4.9273448  5.7267113  5.4836876  5.6952951  6.1602688  5.1779458
## 150  4.6367337  5.2699373  5.0132572  5.2579359  5.7203715  4.8179008
## 151  4.5115523  4.9412165  4.7238880  4.9712864  5.3656830  4.6891453
## 152  4.6403067  5.0355236  4.8337471  5.0327311  5.4684160  4.7862086
## 153  6.0789789  6.4110704  6.3172555  6.3789895  6.6970432  6.2711381
## 154  4.7391689  5.2102456  4.9530824  5.2149874  5.6186780  4.8874945
## 155  6.0164730  6.3733340  6.1708985  6.3904761  6.7180988  6.1312760
## 156  6.7263154  7.1192614  6.9201792  7.1166430  7.3209000  6.9049463
## 157  5.6662142  6.1128193  5.8503238  6.0854157  6.4350630  5.7866856
## 158  4.5328954  4.7849277  4.6975674  4.8899257  5.0439472  4.9098506
## 159  3.7185625  4.0283269  3.8329816  4.0791036  4.4841571  3.9720626
## 160  4.7490116  4.9523399  4.7582984  5.0128320  5.3463250  4.8701801
## 161  5.3994770  5.6377511  5.5425913  5.6763973  5.8993894  5.6627149
## 162  5.3573489  5.5443186  5.5403822  5.6621566  5.6624760  5.7923840
## 163  6.8730398  6.9875066  6.9444542  7.0993180  7.1292125  7.1565086
## 164  7.1281342  7.2774397  7.2225655  7.3989968  7.3990399  7.4258627
## 165  3.1673780  3.8177344  3.6584175  3.8460136  4.2857664  3.6584150
## 166  3.7021742  4.2234362  4.0063118  4.2622673  4.5913615  4.0932181
## 167  5.6227251  5.8168986  5.7492709  5.9517555  5.9788493  5.9840959
## 168  3.4160135  4.1684950  4.0290931  4.1704927  4.4385747  4.0445930
## 169  3.5558437  4.0919547  3.8336111  4.1463229  4.5324072  3.8944415
## 170  3.4275958  3.9874805  3.7297144  4.0472740  4.4534053  3.7826480
## 171  3.3809823  4.0784935  3.7894250  4.0964814  4.5764777  3.7401539
## 172  3.3275785  3.9186721  3.6636652  3.9490597  4.4429285  3.6630514
## 173  2.4940858  2.7667806  2.5747993  2.7735715  3.3736228  2.4465667
## 174  2.6190991  2.5935565  2.4330265  2.6749311  3.1204834  2.5689731
## 175  2.1425206  2.3760722  2.4394221  2.3657335  2.7321993  2.4841968
## 176  2.4459258  2.8315030  3.2685474  2.8227563  2.5044690  3.4421818
## 177  1.6158067  2.3035498  2.6146234  2.2645753  2.3332697  2.6421739
## 178  2.4017128  2.3933430  2.4365751  2.4625918  2.7702644  2.6555309
## 179  2.8791581  2.8771492  2.8756059  2.9832514  3.1609945  3.0941650
## 180  3.5362562  3.1678402  3.3781750  3.2548824  3.1399079  3.6172162
## 181  4.4081212  4.0157807  3.9410086  4.1696113  4.2456926  4.1614943
## 182  2.9827208  2.7552503  2.9706666  2.7824232  2.8305537  3.0601122
## 183  4.1164454  3.5221408  3.4306908  3.6736034  3.8643990  3.7145712
## 184  3.5832870  2.8945670  2.7530988  3.0301491  3.4020220  3.0246623
## 185  2.8461126  2.5495164  2.3723142  2.5787439  3.1781484  2.2869461
## 186  2.4867112  2.3703368  2.4229662  2.4112638  2.6994298  2.4062620
## 187  4.8987688  4.6849962  4.8816071  4.7989849  4.5382911  5.1174864
## 188  2.8788345  4.0268711  4.2891257  4.0577780  3.8899854  4.4254809
## 189  2.7587774  3.9842811  4.3555628  3.9899782  3.7202838  4.5162851
## 190  3.3046848  4.3411976  4.6112326  4.4015169  4.1731417  4.7903091
## 191  3.3306998  4.5527559  4.9545383  4.5950760  4.2233525  5.1283081
## 192  2.8763102  4.1334915  4.4990868  4.1747764  3.9195616  4.6810846
## 193  3.5755562  4.6257515  5.0002823  4.6872053  4.3400049  5.2193314
## 194  3.5040564  4.6842237  5.1234480  4.6919803  4.2984962  5.2650198
## 195  3.3142562  4.4673927  4.8735588  4.4760094  4.1540865  5.0306354
## 196  5.5938423  6.5694578  6.8296409  6.6493488  6.3382055  7.0247946
## 197  4.5709944  6.1314324  6.3678523  6.1931731  6.0041925  6.5341885
## 198  4.2058387  5.9654118  6.1499004  6.0175405  5.8842237  6.2564621
## 199  4.4867527  6.1141018  6.3208990  6.1795070  6.0212099  6.4586176
##             19         20         21         22         23         24
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20   1.6771344                                                       
## 21   2.8186388  1.7947947                                            
## 22   2.3253926  0.8753478  1.3778455                                 
## 23   2.7306608  1.4757338  0.9514578  0.8795849                      
## 24   2.8961673  1.6804166  0.4678080  1.1052409  0.5856703           
## 25   2.5877917  1.2246890  0.9386681  0.6138878  0.5142981  0.5968183
## 26   2.0326047  1.4616627  1.1563890  1.3448369  1.3639767  1.2662570
## 27   2.3120378  1.0179633  1.1134941  0.5518461  0.8421166  0.8895967
## 28   2.2886332  1.5736221  1.2452115  1.2058629  1.0520402  1.1680367
## 29   2.7817191  1.4566608  1.8611169  0.8292822  1.0648474  1.4763267
## 30   2.7022029  1.5419987  2.2163823  1.0691780  1.3913356  1.8595110
## 31   2.8209744  1.9476845  0.4419368  1.5387391  0.9622728  0.6275843
## 32   2.6872770  1.3037004  1.3437198  0.7276457  0.8906101  1.0462541
## 33   3.0169828  2.9849440  1.9986559  2.7204462  2.2504960  2.1955020
## 34   2.5451019  1.4954695  0.4773030  1.1104710  0.8032154  0.5489128
## 35   2.7612187  2.3550322  1.5960194  1.9744028  1.6690282  1.6692873
## 36   2.0528141  1.0693359  2.3037338  1.3982257  1.8974606  2.1575058
## 37   1.7355778  1.0772404  2.2689404  1.4815246  1.9370050  2.1803962
## 38   1.6953707  1.4821613  2.9682682  2.0932323  2.5801050  2.8645760
## 39   1.7682225  1.8820456  3.3037967  2.4347317  2.8838763  3.2030626
## 40   4.5542105  4.6156481  5.7074723  4.8712212  5.2433279  5.5436775
## 41   5.0371100  5.1107364  6.2798373  5.3410869  5.7355388  6.0834310
## 42   3.3441972  3.6310350  5.0238237  4.0545652  4.4356608  4.8403310
## 43   2.8200479  3.2109297  4.6039025  3.7292635  4.1510634  4.4765796
## 44   2.8211445  3.1630670  4.5027623  3.6632478  4.0406653  4.3721619
## 45   2.4124612  2.2874538  3.4336546  2.6504433  3.0099465  3.2864067
## 46   2.2008014  2.2210090  3.3553963  2.7314832  3.0773417  3.2864880
## 47   2.2429526  2.2680439  3.1847896  2.6794511  2.9041503  3.1219548
## 48   3.1345627  2.3133919  2.1391912  2.0366423  1.9146824  1.9770701
## 49   4.1453981  3.5463970  2.4247210  3.2166180  2.7787448  2.5155402
## 50   2.5963801  2.1628004  2.5764830  2.2764178  2.4387309  2.5015463
## 51   3.1135444  2.9309413  3.6107049  3.1229019  3.3067837  3.4867546
## 52   3.2903387  2.8515005  3.6115701  2.9432415  3.2377684  3.4264958
## 53   3.5603862  3.6194229  4.8346590  3.9494843  4.3197482  4.6463524
## 54   3.2025965  3.3457118  4.4432278  3.7295650  4.0702435  4.3168721
## 55   4.2202213  4.0721029  4.4996215  4.1909450  4.2957429  4.4085069
## 56   6.0663730  6.0709113  6.9891381  6.1743722  6.4694673  6.7706390
## 57   5.4101638  5.3493427  6.1264144  5.4991972  5.7633035  5.9593171
## 58   6.3648329  6.2751553  7.0467371  6.3550162  6.6390751  6.8623917
## 59   2.9932559  3.0348045  4.2254262  3.3854531  3.7783598  4.0485307
## 60   2.6088094  2.3476801  3.3817924  2.6548453  3.0079923  3.2212780
## 61   2.7959030  2.2833532  2.8359387  2.3650762  2.6010814  2.6903932
## 62   3.2314929  2.3755298  2.4096214  2.1118498  2.1867328  2.2120770
## 63   3.2107800  2.6088831  3.5796979  2.6349272  3.0308380  3.3058751
## 64   3.4158149  3.1724646  4.1556818  3.2674984  3.5535284  3.8947157
## 65   4.5263082  4.1932985  5.0260188  4.1019497  4.4231130  4.7279797
## 66   5.0005902  5.0858307  6.0255533  5.3732261  5.6630847  5.8980604
## 67   4.7291130  4.7505523  5.3995857  4.9975914  5.1919926  5.3294550
## 68   2.5662114  2.7567625  4.0054205  3.2468014  3.6329353  3.8878246
## 69   2.4141582  2.3919420  3.2353461  2.7971642  3.0248984  3.1723104
## 70   2.4936749  2.4907967  3.6650971  2.9205124  3.2953691  3.5346831
## 71   2.6966036  3.0513094  4.4597186  3.5575774  3.9378581  4.3138265
## 72   2.1235069  2.4984862  3.7736807  3.0422086  3.3917364  3.6853197
## 73   2.5269401  2.9068696  4.3644968  3.4984441  3.9257162  4.2490964
## 74   2.5163096  2.9544481  4.3361768  3.4938460  3.8663260  4.2162093
## 75   2.6920120  3.0358045  4.4443262  3.5811422  3.9663467  4.3257458
## 76   2.3441532  2.0986599  3.3126524  2.4319383  2.8084124  3.1471820
## 77   2.5939998  1.8473596  2.5505739  1.8036936  2.0787147  2.3598529
## 78   2.2218833  1.9600205  3.1145281  2.3190944  2.6688569  2.9803728
## 79   2.3978571  1.9908351  2.9259073  2.1699221  2.4490013  2.7526704
## 80   2.1542767  2.0824875  3.3337752  2.5840340  2.9732251  3.2351485
## 81   3.1593180  3.0463555  4.3726155  3.3152678  3.7559819  4.1458959
## 82   3.1427573  2.4694984  3.4666691  2.4538932  2.8613274  3.1929418
## 83   2.7172093  2.6699141  3.9871306  3.0457375  3.4783272  3.8108433
## 84   2.5687856  2.3160257  3.5313044  2.6282065  3.0647052  3.3558203
## 85   2.4783472  2.1175272  3.3108817  2.3585266  2.7500785  3.1077420
## 86   2.8293637  2.3665001  3.6201080  2.5096894  2.9912712  3.3756922
## 87   2.1519522  1.9058373  2.9476792  2.2299529  2.5471057  2.8271627
## 88   2.3176464  1.7944780  3.0253287  2.0964294  2.5625255  2.8635373
## 89   3.6406774  2.7670865  3.6476001  2.6056204  2.9735341  3.3486295
## 90   3.4836317  2.9411584  4.0613641  2.9460665  3.3644836  3.7879242
## 91   2.7453238  2.0941987  3.1189295  2.1971431  2.5868082  2.9236090
## 92   2.8685761  2.0907691  3.0520900  2.1253691  2.5286207  2.8441146
## 93   2.9336878  2.5299145  3.5987764  2.7272477  3.0862732  3.4178492
## 94   2.8402049  2.8637592  4.1672585  3.2885435  3.7167774  4.0379144
## 95   3.0633362  2.3034350  2.9750647  2.2777577  2.5604888  2.7953756
## 96   2.9090844  2.6170550  3.7761249  2.7386915  3.2135611  3.5760181
## 97   2.6341316  1.9412291  2.7562282  2.0070849  2.3342284  2.5954671
## 98   5.0590037  4.5142644  5.4387497  4.3152116  4.6686193  5.1091905
## 99   4.8757677  4.7319967  5.9199279  4.7660457  5.1935235  5.6461610
## 100  3.9850811  3.5036536  4.5477909  3.4355771  3.8184021  4.2566445
## 101  2.8641884  1.9351248  2.9317740  1.7342001  2.2240106  2.6454635
## 102  2.7718126  1.9450966  3.1388170  1.9031592  2.4101173  2.8587043
## 103  3.3338078  3.7519365  3.9719752  3.6985195  3.8721982  4.0149527
## 104  2.4741547  1.1711577  1.6959207  0.8400769  1.1810324  1.4793855
## 105  2.5701715  1.2924717  1.8741684  0.9800151  1.3804511  1.6621775
## 106  2.7485581  1.5539398  1.3893677  1.1454727  1.2565280  1.3014235
## 107  2.7018774  1.6034448  1.2617503  1.2213336  1.1743147  1.2126031
## 108  2.4627788  1.3180688  1.8010447  1.0721664  1.3593973  1.6402243
## 109  2.9595674  1.6791411  2.0841084  1.2141864  1.4602912  1.8023823
## 110  2.6712735  1.4447617  1.6028454  0.9731500  1.0733463  1.3791479
## 111  1.8355039  1.1942240  2.4035434  1.5180358  1.8701233  2.2616144
## 112  3.2268698  2.3653877  3.0862648  2.2081718  2.4859218  2.8415668
## 113  3.0883843  2.1415994  2.1076254  1.9073206  1.9657758  2.0319698
## 114  3.2252790  2.2379769  2.1108579  1.9126793  1.8871896  1.9904778
## 115  2.9692221  2.0634606  2.6654273  2.0027028  2.2640304  2.5072097
## 116  2.7979616  2.1081422  2.1430886  1.9454093  2.0292703  2.1164465
## 117  2.6696107  1.9150227  2.6477957  1.9444966  2.2371172  2.5011405
## 118  2.7972614  1.8826785  2.5517301  1.8824123  2.2223767  2.4119963
## 119  2.4207488  2.0094111  2.3658036  2.0380228  2.2187392  2.3608948
## 120  2.3758393  1.8053660  2.4564178  2.0171385  2.2718025  2.4220953
## 121  3.4099410  2.9855265  3.3835184  3.0413260  3.2162413  3.3430079
## 122  3.6176829  3.0379662  3.2593644  2.9659364  3.0915583  3.1998900
## 123  3.8566432  3.2233235  3.1219004  3.0330020  3.0416790  3.0878429
## 124  4.2738187  3.7034939  3.0784047  3.4346758  3.1838594  3.1311960
## 125  3.8951799  3.2280299  3.0770675  3.0435081  3.0403486  3.0576929
## 126  3.7393180  3.1093184  3.2676723  2.9942125  3.1162376  3.2074567
## 127  4.3523966  3.8731051  3.1282834  3.6435596  3.3590841  3.2482272
## 128  3.5650916  2.7757676  2.5550503  2.6187710  2.5993608  2.5700098
## 129  3.8201218  2.9128490  2.9110663  2.6273539  2.6042253  2.7692605
## 130  3.5941830  2.8098649  2.4776149  2.6631463  2.5715448  2.5152609
## 131  3.7575121  2.8336776  3.0362442  2.5743345  2.6744745  2.8640928
## 132  3.6538704  2.7342072  2.9724045  2.5025200  2.6436684  2.8122994
## 133  3.6501239  2.7919821  3.1535153  2.5553548  2.7951929  2.9807908
## 134  3.4140636  2.5907834  2.5907691  2.4183867  2.5130594  2.5387186
## 135  3.4061714  3.0768810  2.7550070  2.9050633  2.8859670  2.8457745
## 136  3.7555178  2.8697586  2.7581397  2.5664981  2.5005102  2.6341157
## 137  3.4748892  2.7194506  2.5980983  2.5317281  2.5184873  2.5673735
## 138  3.8039500  2.8953388  2.9349081  2.6279548  2.6142399  2.7889408
## 139  3.8687087  3.0870910  2.5309907  2.8478669  2.6042397  2.5638317
## 140  3.7786545  2.9312288  2.6964938  2.6529173  2.5513325  2.6282887
## 141  4.0097156  3.2940477  2.6902184  3.0089411  2.6567160  2.6928858
## 142  4.8796288  4.3921553  3.2588999  4.1545105  3.7552993  3.4907795
## 143  6.9515487  6.5739539  6.1283881  6.4508461  6.2859126  6.2011284
## 144  5.6788460  5.2124837  4.6832239  5.0457515  4.8591488  4.7638408
## 145  5.9079641  5.5219068  4.8541360  5.4115541  5.1886810  5.0099541
## 146  5.8597324  5.8261514  5.2589250  5.6220106  5.3930285  5.3683168
## 147  5.3504063  5.3646982  5.1593201  5.2891556  5.3053023  5.2668316
## 148  5.8277989  5.4737727  4.8373876  5.3584880  5.1579474  4.9879799
## 149  5.5998504  5.3113893  4.7584109  5.1795298  5.0146755  4.8880748
## 150  5.2917331  4.9208758  4.6009224  4.8112548  4.7154017  4.6667833
## 151  5.2392834  4.7478875  4.8182246  4.6227637  4.7010626  4.7674417
## 152  5.1392599  4.7674301  4.7697873  4.7195115  4.8471845  4.8061089
## 153  6.3874627  6.1870110  6.2373877  6.2495070  6.3570449  6.3026618
## 154  5.1307690  4.9408390  4.8447842  4.8495652  4.9097430  4.8976550
## 155  6.4916093  6.1970611  6.1741667  6.1109399  6.1214319  6.1626443
## 156  6.7350455  6.9533025  6.9353370  6.9332822  6.9543369  7.0031471
## 157  5.5557130  5.8099344  5.6072278  5.8081036  5.8413242  5.7699136
## 158  5.3679635  4.8999431  5.5639271  4.7239636  5.1340737  5.3682199
## 159  4.4649601  3.9161917  4.3534448  3.8409476  4.1585583  4.2621578
## 160  5.4092522  4.8873932  5.2291720  4.7756518  4.9728678  5.1126655
## 161  5.9293295  5.6079394  6.0261407  5.5732757  5.8303693  5.9448917
## 162  6.1707153  5.7721368  6.5698095  5.6044290  6.0451412  6.3360673
## 163  7.5930108  7.1810804  7.8135856  6.9969564  7.3324835  7.5913214
## 164  7.9052874  7.4957255  8.1123716  7.2860417  7.5662712  7.8671614
## 165  4.2386774  3.6444850  3.9140884  3.5720106  3.7810368  3.8455353
## 166  4.2406371  4.0987623  4.3946658  4.0194289  4.2721897  4.3695599
## 167  6.4828440  6.0410199  6.7417157  5.8042205  6.1722469  6.4868372
## 168  3.9517703  4.0138136  4.2929804  4.0212265  4.2389925  4.3189196
## 169  4.3295222  3.9540706  4.2005845  3.8125308  4.0033543  4.1295614
## 170  4.3464690  3.8590245  4.1090579  3.7089543  3.8681031  4.0117669
## 171  4.1459716  3.8153752  3.7978708  3.7166041  3.7880678  3.8119255
## 172  4.2248133  3.6966543  3.8234707  3.5978685  3.7452584  3.7863715
## 173  3.1610987  2.4314341  2.6311452  2.3443845  2.5952574  2.6011996
## 174  3.3491579  2.5577131  3.2582057  2.4648483  2.8063513  3.0635189
## 175  2.8147217  2.2706768  3.1051073  2.4415057  2.8358259  3.0138882
## 176  3.1831064  3.1425028  4.4436609  3.4573224  3.9127378  4.2774874
## 177  2.6129424  2.3885879  3.4250448  2.6970969  3.0596668  3.3183026
## 178  3.1605896  2.5128387  3.5008959  2.5795472  3.0391743  3.3077669
## 179  3.6543420  3.0601593  3.9877157  2.9885390  3.3978405  3.7461548
## 180  3.8381218  3.4807610  4.6277532  3.5092807  4.0070863  4.3879758
## 181  4.8555696  4.2693937  5.0542427  4.0128517  4.3487640  4.7504065
## 182  3.1884731  2.8595111  3.8571689  2.9339040  3.4599669  3.7108344
## 183  4.4168889  3.7405991  4.5949948  3.5148635  3.9840581  4.3153841
## 184  3.8087661  3.0079817  3.8264067  2.8087880  3.3291745  3.5830509
## 185  3.0172351  2.2735030  2.5916614  2.1409453  2.5068350  2.5284025
## 186  2.8511381  2.3597380  3.1037475  2.3341595  2.7182312  2.9566668
## 187  5.3123429  5.0764237  6.1286938  4.9988461  5.4410862  5.8527222
## 188  4.4143326  4.2871352  5.2535188  4.4210658  4.7646023  5.0778042
## 189  4.2707317  4.3021883  5.3835510  4.5500393  4.9292459  5.2290419
## 190  4.8339450  4.6949690  5.7005176  4.7839273  5.1307674  5.4824801
## 191  4.9001862  4.9954273  6.0651693  5.1641933  5.5416624  5.8677513
## 192  4.5688226  4.5462861  5.5844398  4.7304298  5.0893458  5.3909423
## 193  5.1058189  5.0976830  6.2005719  5.2422760  5.6286223  5.9751672
## 194  4.9465087  5.0867822  6.1554048  5.3417482  5.6689151  5.9855399
## 195  4.7227745  4.8467426  5.8915849  5.1023351  5.4456111  5.7344617
## 196  7.0278492  6.9729584  7.9101311  6.9843625  7.3365340  7.6760738
## 197  6.5810038  6.4942378  7.3051327  6.5632216  6.8264819  7.1032867
## 198  6.2748991  6.2612214  6.9205464  6.3099347  6.5051715  6.7528490
## 199  6.5483848  6.4521046  7.1876949  6.4837356  6.7230715  6.9895265
##             25         26         27         28         29         30
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26   1.1534378                                                       
## 27   0.3913349  0.9601190                                            
## 28   1.0108345  0.6641659  0.9385630                                 
## 29   0.9995264  1.7573289  1.0523239  1.3384639                      
## 30   1.3924842  2.0152347  1.3949992  1.5713712  0.4898614           
## 31   1.0564778  1.1217431  1.2207035  1.1077362  1.9004252  2.2368968
## 32   0.6037321  1.2718750  0.6576296  1.0614166  0.7875682  1.2096483
## 33   2.4472033  1.8403745  2.4773802  1.7161003  2.9023792  3.0495131
## 34   0.7046486  0.8206851  0.8166324  0.8817912  1.5550316  1.9046474
## 35   1.7614146  1.1956323  1.7656626  0.9001024  2.0461423  2.2301084
## 36   1.7412560  2.0238046  1.6178847  2.0255673  1.7125466  1.7012390
## 37   1.8117644  1.9205585  1.6593397  1.9631248  1.8803837  1.8427786
## 38   2.4416296  2.5352724  2.2534003  2.6033366  2.4075718  2.2884205
## 39   2.8110515  2.8887636  2.6364328  2.9077325  2.7231570  2.5239326
## 40   5.1747672  5.3079272  5.0355235  5.2204924  4.8586586  4.6420737
## 41   5.6865250  5.8612216  5.5512612  5.7170884  5.2520847  4.9780207
## 42   4.3878202  4.4804357  4.2160452  4.3663273  4.0020694  3.7121064
## 43   4.0446615  4.0451178  3.8373808  4.0515567  3.8375044  3.6192552
## 44   3.9572828  3.9901501  3.7683066  3.9816574  3.7696981  3.5581815
## 45   2.8799827  2.9682074  2.6975102  2.9584837  2.7679517  2.6624786
## 46   2.9333440  2.9286092  2.7472441  3.0470821  3.0191043  2.9669867
## 47   2.8339012  2.8504768  2.6887803  2.9179440  2.9657652  2.9125550
## 48   1.8765272  2.1824737  1.8947483  2.0581878  2.1270887  2.3190899
## 49   2.8441632  2.9337574  2.9523788  2.9714701  3.5129477  3.7913446
## 50   2.2848111  2.3696537  2.1493557  2.4627463  2.5856542  2.6868696
## 51   3.1969285  3.2760838  3.0593180  3.2761777  3.2319425  3.2229475
## 52   3.0671545  3.2430600  2.9189403  3.1956934  2.9428937  2.9361959
## 53   4.2134994  4.3330756  4.0380586  4.2552489  3.9063196  3.7117571
## 54   3.9394672  3.9726606  3.7504437  3.9976616  3.8405690  3.7208683
## 55   4.2071905  4.2576955  4.1064529  4.2691514  4.2808219  4.3012193
## 56   6.4102572  6.5921303  6.2822015  6.4215875  6.0073348  5.7975967
## 57   5.6306322  5.7264412  5.4838159  5.6775679  5.4335061  5.3535541
## 58   6.5454539  6.6954808  6.4246073  6.5847698  6.2422211  6.1074446
## 59   3.6013719  3.6660056  3.3785541  3.6558450  3.4075123  3.2832935
## 60   2.8054929  2.9025287  2.5988340  2.9339099  2.7573785  2.7353198
## 61   2.3736254  2.4961859  2.1959078  2.5504450  2.5241458  2.6329075
## 62   1.9747296  2.2110509  1.8892687  2.1381474  2.1060630  2.3360046
## 63   2.8344970  3.1367598  2.6662034  2.9868228  2.4507477  2.3788981
## 64   3.4620540  3.7038390  3.3102277  3.5062620  3.0728286  2.9024112
## 65   4.3213163  4.6314090  4.1846941  4.3766330  3.8162592  3.6283338
## 66   5.5662817  5.6208827  5.4249851  5.6038504  5.3873569  5.2626498
## 67   5.0904302  5.0923791  4.9682270  5.1448050  5.1129379  5.0841175
## 68   3.4765988  3.4829009  3.2604431  3.5479167  3.4130774  3.2976237
## 69   2.8658279  2.8281230  2.6795780  2.9659413  3.0677615  3.0923103
## 70   3.1242796  3.1662487  2.9135291  3.2218992  3.0768586  2.9976236
## 71   3.8772009  3.9153470  3.6940802  3.8636206  3.6104359  3.3591173
## 72   3.2986926  3.2456935  3.0999828  3.2919388  3.2433566  3.0880612
## 73   3.8108894  3.8068806  3.6031495  3.8445239  3.6438681  3.4443725
## 74   3.7957473  3.7799113  3.6027278  3.7679230  3.6005340  3.3752896
## 75   3.9172990  3.9630136  3.7513875  3.9447416  3.7066322  3.4654406
## 76   2.7297255  2.8754237  2.5822783  2.7920290  2.4973515  2.3312167
## 77   2.0202143  2.2880879  1.9507207  2.1188223  1.8345601  1.7941889
## 78   2.6011348  2.7320014  2.4667151  2.6869460  2.4752082  2.3433289
## 79   2.3853620  2.5769148  2.2621515  2.4693141  2.2507270  2.1531750
## 80   2.8503789  2.9077705  2.6766836  2.9674045  2.8255837  2.7251681
## 81   3.6821750  3.9093867  3.5265509  3.7497965  3.2238207  2.9419062
## 82   2.7459984  3.1140266  2.6321921  2.9003396  2.2652647  2.1082158
## 83   3.3687128  3.5136276  3.1909253  3.4539412  3.0943681  2.8921528
## 84   2.9195703  3.0710739  2.7387796  3.0279057  2.6975404  2.5601854
## 85   2.6825206  2.9322582  2.5476036  2.7985585  2.3838375  2.1863752
## 86   2.9134264  3.2282227  2.7835868  3.0320530  2.4103331  2.1378724
## 87   2.4890466  2.6362051  2.3573743  2.6109882  2.4686586  2.3591063
## 88   2.4514327  2.6784726  2.3158505  2.6264030  2.2545731  2.1202627
## 89   2.9426894  3.4267974  2.9220443  3.1121441  2.2750005  2.0652392
## 90   3.3634733  3.7662430  3.3000335  3.4733239  2.7145674  2.3835169
## 91   2.5482871  2.8652985  2.4804972  2.7029348  2.2162189  2.0479906
## 92   2.4671495  2.8219481  2.4082421  2.6552398  2.1176963  1.9838330
## 93   3.0418520  3.2866163  2.9490690  3.1562261  2.7392255  2.5623383
## 94   3.6446581  3.7595162  3.4969670  3.7309132  3.4179564  3.2062789
## 95   2.4966237  2.8214399  2.4553185  2.6943404  2.3242495  2.2906615
## 96   3.1632821  3.3637911  3.0367170  3.1724634  2.6844646  2.3955883
## 97   2.2760961  2.5592360  2.2096695  2.4553233  2.1446538  2.0790294
## 98   4.7260374  5.2167479  4.7065371  4.7987000  3.9018076  3.5207880
## 99   5.2361720  5.5925401  5.1550338  5.2688479  4.5256102  4.0978951
## 100  3.8553787  4.2848223  3.8082161  3.9396681  3.1479139  2.7775761
## 101  2.2389809  2.7723157  2.2169286  2.4466342  1.5730131  1.2130324
## 102  2.4090991  2.8905817  2.3584014  2.5881898  1.7239502  1.3380369
## 103  3.8412676  3.1124367  3.6739440  2.9852305  3.6355846  3.5393053
## 104  1.1691497  1.7476182  1.2292378  1.5555300  1.1327773  1.2119579
## 105  1.3525926  1.9029771  1.3993122  1.7116831  1.2139584  1.2521553
## 106  1.2815208  1.7718248  1.4123850  1.6898627  1.6218261  1.7932580
## 107  1.2836621  1.7429745  1.4384443  1.6588144  1.7247142  1.8889855
## 108  1.4083744  1.8753167  1.4699988  1.6968764  1.3947634  1.4079977
## 109  1.5102094  2.1612724  1.6211665  1.8366573  1.1066225  1.1161907
## 110  1.1885758  1.7949139  1.3280558  1.5253549  1.1813208  1.2733628
## 111  1.9084344  2.1871136  1.8441734  2.0652329  1.7963624  1.6193807
## 112  2.5217892  2.9796077  2.5382258  2.6951804  2.0648878  1.8986347
## 113  1.9851606  2.3294934  2.0636227  2.2543932  2.1895784  2.3080345
## 114  1.9572617  2.3730660  2.0713279  2.2173665  2.0961401  2.2131302
## 115  2.2421706  2.5845303  2.2520607  2.4432244  2.0785921  2.0645288
## 116  2.0364468  2.1076180  2.0466016  2.0413320  2.2048159  2.2875615
## 117  2.2239438  2.5359039  2.1979301  2.4176545  2.1126220  2.0473213
## 118  2.1292213  2.4471182  2.0962439  2.3872827  2.0728516  2.0950577
## 119  2.2203537  2.1866379  2.1681228  2.1674513  2.3627357  2.3606439
## 120  2.2167592  2.3513584  2.1573862  2.4087730  2.4091523  2.4271303
## 121  3.2144084  3.3599619  3.1957530  3.3460991  3.2911914  3.2717765
## 122  3.0964654  3.2726623  3.1081924  3.2107288  3.1383830  3.1554856
## 123  3.0915984  3.2863222  3.1497371  3.2081694  3.2256286  3.2858050
## 124  3.3299976  3.4529613  3.4557668  3.3795482  3.6613625  3.7888912
## 125  3.0755479  3.2587000  3.1381875  3.2067847  3.2498720  3.3395661
## 126  3.1280980  3.3435953  3.1549148  3.2759371  3.1784153  3.2004563
## 127  3.5002773  3.5242707  3.6203344  3.5151172  3.9343747  4.0863603
## 128  2.6164007  2.8189439  2.6968782  2.8291788  2.9192087  3.0659288
## 129  2.7050007  3.1048181  2.8236015  2.8894293  2.6314223  2.6757769
## 130  2.6003435  2.7881463  2.6945927  2.8184827  2.9756326  3.1507577
## 131  2.7158132  3.1239701  2.7939738  2.9117811  2.5392065  2.5549800
## 132  2.6551149  3.0475447  2.7148218  2.8729142  2.5205575  2.5466145
## 133  2.7834031  3.1548604  2.8086371  2.9675063  2.5582517  2.5278155
## 134  2.4829314  2.7271783  2.5230078  2.6994193  2.6606086  2.7762412
## 135  2.8809676  2.5833310  2.8617175  2.5875773  3.1096447  3.2242640
## 136  2.6075474  2.9862226  2.7292173  2.7851113  2.6128732  2.6812607
## 137  2.5663329  2.7758758  2.6411526  2.7062691  2.7464876  2.8467886
## 138  2.7048306  3.0933286  2.8171509  2.8782328  2.6105673  2.6560228
## 139  2.7284656  2.9425973  2.8795528  2.8877014  3.0824493  3.2556894
## 140  2.6694647  3.0051403  2.8018039  2.8575853  2.7964072  2.8875405
## 141  2.8810185  3.1231619  3.0636803  2.9659265  3.1569324  3.2843762
## 142  3.9128488  3.9375477  4.0730223  4.0329271  4.5870306  4.8073196
## 143  6.3555919  6.4120320  6.4377053  6.4360375  6.6529642  6.7711414
## 144  4.9481043  5.0376103  5.0475964  5.0528075  5.2913591  5.4215882
## 145  5.2547955  5.2482916  5.3474628  5.3608625  5.7518933  5.9310523
## 146  5.5252070  5.2275568  5.5678386  5.1420095  5.6988846  5.7571136
## 147  5.2959404  4.9262930  5.2508933  4.9592486  5.4313940  5.4832522
## 148  5.2243421  5.2160045  5.3082027  5.3210779  5.7053088  5.8676276
## 149  5.0889399  5.0489484  5.1554509  5.1122677  5.4882801  5.6110770
## 150  4.7660421  4.7666865  4.8194403  4.7823710  5.0194915  5.1180208
## 151  4.7175468  4.8751012  4.7461715  4.7984816  4.7049775  4.7160357
## 152  4.7878829  4.7747122  4.7714905  4.8400988  4.9427140  5.0134621
## 153  6.2841367  6.2022309  6.2514047  6.3267857  6.4838765  6.5611356
## 154  4.8996064  4.7414500  4.8772388  4.7488115  5.0042778  5.0441845
## 155  6.1416989  6.1556454  6.1574326  6.1033444  6.1597275  6.1843337
## 156  6.9714613  6.5859986  6.9089194  6.5566022  6.9642272  6.9415851
## 157  5.7992377  5.2340232  5.7098755  5.3421860  5.9898665  6.0500266
## 158  5.1076140  5.4172506  5.0627753  5.1950493  4.6295991  4.4080959
## 159  4.0726265  4.2239409  4.0306188  4.1674368  3.9146981  3.8832657
## 160  4.9518335  5.1516442  4.9499873  5.0243486  4.7377029  4.6894236
## 161  5.7759365  5.8729015  5.7311916  5.8070882  5.5990742  5.5334722
## 162  6.0359979  6.3938586  5.9850881  6.1218259  5.4375096  5.1431081
## 163  7.3420280  7.6973693  7.3192674  7.4297505  6.8085497  6.5715845
## 164  7.6174512  7.9996177  7.6137461  7.6745579  7.0243760  6.7627861
## 165  3.7244319  3.9302776  3.7133724  3.9072834  3.7381577  3.7598890
## 166  4.2168647  4.0543073  4.1268910  3.9891955  4.0833872  4.0217844
## 167  6.2063434  6.5976778  6.1839802  6.2630922  5.5579095  5.2546051
## 168  4.1914322  3.9107600  4.0835940  3.9054469  4.1672556  4.1143852
## 169  3.9908238  4.0154724  3.9582702  3.8895188  3.8289544  3.7769913
## 170  3.8687408  3.9883573  3.8604387  3.8430752  3.6994527  3.6591716
## 171  3.7634403  3.6537129  3.7380014  3.6351286  3.8460315  3.9015343
## 172  3.6933902  3.7676982  3.6795249  3.7447381  3.7282528  3.7796529
## 173  2.5115017  2.7336572  2.4933024  2.7811979  2.7307168  2.8056927
## 174  2.7690998  3.1442156  2.7495121  2.9685042  2.4608884  2.3601503
## 175  2.7367651  2.9244044  2.6506038  2.9350185  2.7058840  2.6544512
## 176  3.8759283  4.0599867  3.7482131  3.9452140  3.4980699  3.2102565
## 177  2.9930060  3.1265942  2.8748352  3.1124507  2.9047297  2.7786702
## 178  2.9335370  3.2422883  2.8425320  3.1253116  2.6029294  2.4671585
## 179  3.3872548  3.7739122  3.3387341  3.5173253  2.8496575  2.5888413
## 180  3.9950170  4.3568024  3.9097815  4.1128704  3.4075154  3.0515233
## 181  4.4258636  4.9221993  4.4269335  4.5179508  3.6848883  3.3265782
## 182  3.4037712  3.6764453  3.2989707  3.5813059  3.1376715  2.8983986
## 183  3.9650522  4.4342616  3.9276125  4.1240883  3.2961472  2.9960139
## 184  3.2396758  3.6826634  3.1839191  3.4702040  2.7352345  2.5420886
## 185  2.3873039  2.6333173  2.3325410  2.6615942  2.5374591  2.5798716
## 186  2.6923018  2.9672621  2.6187408  2.8429260  2.5288116  2.3738951
## 187  5.4808035  5.8733736  5.4129400  5.5382471  4.7729539  4.3589955
## 188  4.7492176  4.9635322  4.6594244  4.8092718  4.3838423  4.1487705
## 189  4.8671597  4.9887701  4.7339849  4.8993162  4.5499997  4.3321622
## 190  5.1236091  5.3843198  5.0335171  5.1715203  4.6475827  4.3731096
## 191  5.4873908  5.6386174  5.3416764  5.4851908  5.0753066  4.8117324
## 192  5.0088923  5.1666421  4.8667211  5.0439797  4.6488882  4.4424535
## 193  5.5727997  5.7803984  5.4372573  5.5971230  5.0919429  4.8199807
## 194  5.6198302  5.7386925  5.4826527  5.6309260  5.2914481  5.0655369
## 195  5.3684635  5.4463260  5.2186303  5.3663162  5.0696769  4.8718323
## 196  7.3362951  7.6069002  7.2458742  7.3603509  6.7982446  6.4969834
## 197  6.7833613  6.9760016  6.6865998  6.8077883  6.4022105  6.2189775
## 198  6.4798470  6.5854410  6.3863457  6.4275825  6.1751403  6.0204942
## 199  6.6934111  6.8886214  6.6053634  6.7100070  6.3291663  6.1500824
##             31         32         33         34         35         36
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32   1.4730434                                                       
## 33   1.6674343  2.6794356                                            
## 34   0.6344059  0.9796073  1.9942363                                 
## 35   1.4034469  1.7574336  1.1965885  1.3664254                      
## 36   2.4429101  1.7125927  3.3612560  2.0162039  2.7074395           
## 37   2.3727840  1.8733081  3.1449862  2.0033298  2.6076942  0.4398399
## 38   3.0394482  2.5111938  3.7487395  2.7085017  3.3045509  1.0277743
## 39   3.3405956  2.9309363  3.8839634  3.0759759  3.5607437  1.5104245
## 40   5.7064531  5.1768201  6.0794468  5.4956760  5.7383414  4.2358416
## 41   6.2727858  5.6566120  6.6006741  6.0491613  6.2293048  4.7080229
## 42   4.9709869  4.4040443  5.2941909  4.7527062  4.9855667  3.1518686
## 43   4.5779479  4.1095672  4.9723067  4.3555452  4.6973168  2.7675248
## 44   4.4655506  4.0503079  4.8665971  4.2705577  4.6300247  2.7231301
## 45   3.4134222  2.9636787  4.0021403  3.2012637  3.6398662  1.7516393
## 46   3.3692605  3.0693646  3.9939386  3.1542875  3.7089542  1.7355795
## 47   3.1530332  3.0519272  3.6916259  3.0324129  3.5389226  1.8360015
## 48   2.0659668  2.1043948  2.8913507  2.0831851  2.5676922  2.0042303
## 49   2.2860058  3.2775879  2.8264286  2.7027215  3.1171299  3.5525974
## 50   2.5494906  2.5558855  3.3081484  2.4951064  3.0932663  1.8670040
## 51   3.5430961  3.3593397  4.0914780  3.4667500  3.8792355  2.4468837
## 52   3.5925082  3.1023097  4.2688464  3.4148039  3.8248394  2.2789796
## 53   4.7904733  4.2374116  5.2415440  4.5917885  4.8968507  3.0587645
## 54   4.4031750  4.0479376  4.8787767  4.2471643  4.6391652  2.8465423
## 55   4.4306665  4.3579563  4.8768127  4.4070735  4.7442823  4.2066664
## 56   6.9195694  6.4215794  7.2020504  6.8008675  6.9208361  5.7301147
## 57   6.0684984  5.6622610  6.4873948  5.9569160  6.2055314  5.0478143
## 58   7.0114916  6.5354116  7.3632664  6.8764729  7.0394530  5.8036707
## 59   4.1675225  3.6745041  4.7025691  3.9932857  4.3734201  2.8930021
## 60   3.3512914  2.8997794  4.0498021  3.1639727  3.6686678  2.2221315
## 61   2.7945684  2.5497210  3.5969848  2.6942396  3.2513455  2.2759961
## 62   2.3649801  2.0512826  3.2471272  2.2681704  2.7266400  2.3624920
## 63   3.5584320  2.7797879  4.2957923  3.3226961  3.7036020  2.3910743
## 64   4.0532463  3.5151438  4.5425989  3.9323859  4.1831603  2.9863582
## 65   4.9387431  4.3289417  5.3872254  4.8309164  4.9739914  3.8494880
## 66   6.0018676  5.5883740  6.3856720  5.8332422  6.1114914  4.6303952
## 67   5.3725186  5.1834190  5.7827007  5.2707485  5.6079856  4.3616039
## 68   3.9760172  3.5932369  4.5127863  3.7878292  4.2473311  2.4959608
## 69   3.1856970  3.0819689  3.8109216  3.0845189  3.6412110  2.2424730
## 70   3.6397939  3.2357634  4.2482400  3.4476996  3.9352173  2.2199431
## 71   4.4174252  3.9318503  4.7787286  4.1968937  4.5005879  2.7772703
## 72   3.7368358  3.4246746  4.1527326  3.5447606  3.9345021  2.3048059
## 73   4.3545682  3.8708204  4.8100212  4.1058893  4.5115856  2.6623327
## 74   4.2929347  3.8727412  4.6420236  4.0821673  4.3989749  2.7110361
## 75   4.4379497  3.9767844  4.8328223  4.1948137  4.5553627  2.7607994
## 76   3.3191448  2.7411935  3.8890527  3.0433454  3.4291370  1.7815768
## 77   2.5852630  1.9934201  3.2811936  2.2991227  2.6777173  1.5567568
## 78   3.1362950  2.6519518  3.7307617  2.8667779  3.3077170  1.6560899
## 79   2.9017465  2.4800919  3.5099908  2.7047234  3.1120101  1.7660033
## 80   3.3657272  2.9335545  3.9936104  3.1006113  3.6260911  1.8526740
## 81   4.3629369  3.6582204  4.8517340  4.1039503  4.3915186  2.5857289
## 82   3.4866232  2.6485107  4.1849858  3.1991723  3.5394961  1.9764096
## 83   3.9861045  3.3979782  4.5291023  3.7345865  4.1225260  2.2421406
## 84   3.5457741  2.9346375  4.1762714  3.2769903  3.7045438  1.8742767
## 85   3.3145137  2.7185822  3.9204607  3.0625805  3.4621973  1.4530768
## 86   3.6564083  2.8352585  4.2636095  3.3384409  3.6629887  1.6595635
## 87   2.9555449  2.6449681  3.5623767  2.7566681  3.2482167  1.3118120
## 88   3.1069939  2.4344579  3.8279612  2.7613592  3.2661838  0.9242053
## 89   3.7246627  2.6909216  4.4174527  3.3544950  3.6048504  2.0099682
## 90   4.1086597  3.2172843  4.6494417  3.7815589  3.9940441  2.1966475
## 91   3.2020859  2.4645561  3.8744820  2.8536728  3.2478992  1.1666171
## 92   3.1554759  2.3388935  3.8905456  2.7808707  3.1953288  1.1626582
## 93   3.6443583  2.9998556  4.2320308  3.3475612  3.7096579  2.1362426
## 94   4.2132313  3.6533871  4.7174090  3.9212974  4.3113304  2.5132990
## 95   3.0578046  2.4486436  3.8053270  2.7620570  3.2032948  1.9711858
## 96   3.8241743  3.0586514  4.2767279  3.4925582  3.6771706  1.8393115
## 97   2.8359084  2.2784966  3.5625164  2.5349736  3.0049815  1.0432911
## 98   5.4603964  4.5461950  5.8489374  5.1891609  5.1939967  3.9227672
## 99   5.9300722  5.1496371  6.2104649  5.6743206  5.7224979  4.1665768
## 100  4.5738856  3.7282626  5.0197414  4.2910248  4.4125901  2.8284493
## 101  3.0363381  2.0939737  3.7369843  2.6619670  2.9830328  1.8931136
## 102  3.2300186  2.2435115  3.9064923  2.8382568  3.1610313  1.8626975
## 103  3.8879427  3.5756874  3.2058173  3.6220111  2.6117806  3.8571704
## 104  1.8723175  1.1281542  2.8847670  1.4357478  2.1299116  1.4508236
## 105  2.0705098  1.2334551  3.0464313  1.6081548  2.2427640  1.4992761
## 106  1.6592839  1.3826241  2.7275687  1.2864049  2.0705138  1.8664506
## 107  1.4918057  1.5147217  2.5301231  1.2344093  2.0188614  1.9475618
## 108  1.9822198  1.3973154  2.8762359  1.5703866  2.1727074  1.5446678
## 109  2.2398296  1.2959624  3.1666487  1.8195813  2.3032101  1.7786626
## 110  1.7537641  1.2030972  2.7161619  1.3938665  1.9995796  1.6909294
## 111  2.4701053  2.0036774  3.1450927  2.1567066  2.6795001  1.3954882
## 112  3.1701924  2.3831675  3.8446418  2.8390718  3.1451308  1.8789984
## 113  2.2687066  2.0511240  3.1261583  2.0182785  2.5842942  1.9004795
## 114  2.2350287  2.0220807  3.0709657  2.0278441  2.5306064  1.9967172
## 115  2.8052172  2.1066726  3.5859486  2.4193306  2.8706581  1.6136195
## 116  2.2451235  2.0500775  2.8433168  1.9782180  2.2871956  1.8749994
## 117  2.7543627  2.2177921  3.4835110  2.4350522  2.9112112  1.4769837
## 118  2.7102550  2.0447107  3.5724328  2.3217941  2.8849200  1.4652931
## 119  2.4425286  2.2857121  2.9095292  2.1877463  2.4720413  1.7487480
## 120  2.5774616  2.3256562  3.3244199  2.2948041  2.8994553  1.5031436
## 121  3.4816246  3.2839946  4.0278448  3.2772881  3.6721821  3.1603660
## 122  3.3617576  3.1038472  3.9238334  3.1428569  3.4723445  3.2040036
## 123  3.2154074  3.1562426  3.7428165  3.0787951  3.3774504  3.4198506
## 124  3.1044018  3.5099251  3.4376948  3.1636665  3.3649845  3.9533475
## 125  3.1849862  3.1268336  3.7552802  3.0357304  3.3671481  3.4339865
## 126  3.3865625  3.1438682  3.9740594  3.1741449  3.5215812  3.2710984
## 127  3.1494436  3.7114315  3.4027393  3.2502086  3.4419689  4.1518610
## 128  2.7158969  2.6802531  3.4629984  2.5215183  3.0272962  3.3385333
## 129  3.0144660  2.6475101  3.6835410  2.7906745  3.1064146  3.3429404
## 130  2.6224596  2.6981513  3.3856925  2.4716239  3.0101551  3.3947498
## 131  3.1540359  2.5976223  3.8636780  2.8695624  3.1958332  3.2505800
## 132  3.1045884  2.5485198  3.8522408  2.8091948  3.1860374  3.1832848
## 133  3.2877688  2.6595644  3.9787297  2.9749077  3.2870225  3.2098680
## 134  2.7409443  2.5038457  3.5161429  2.5014782  2.9874693  3.1641345
## 135  2.7908216  2.8394194  2.9148544  2.6195923  2.4739711  3.6314284
## 136  2.8474358  2.6035382  3.5085874  2.6693212  2.9936477  3.3417212
## 137  2.7170853  2.6009335  3.3648437  2.5206803  2.9015774  3.2616446
## 138  3.0366284  2.6203611  3.7090198  2.7938684  3.1030773  3.3210814
## 139  2.6242101  2.8446413  3.2563552  2.5618658  2.9662274  3.6228364
## 140  2.8055920  2.7145497  3.4588993  2.6542813  3.0194905  3.4183287
## 141  2.7059813  3.0305675  3.1447853  2.7347541  2.9823744  3.7852046
## 142  3.2993216  4.2556456  3.5972399  3.5557875  3.9100017  4.9362891
## 143  6.1706949  6.4751382  6.4243028  6.2107914  6.4174142  6.6071574
## 144  4.7404328  5.0971716  5.0657802  4.7855548  5.0406988  5.2462861
## 145  4.9149546  5.4557123  5.2243829  5.0065913  5.3212136  5.6138895
## 146  5.1768278  5.5534558  4.7175327  5.2379194  4.7830230  5.8439705
## 147  5.1718186  5.2230571  4.9799012  5.0500018  4.7442679  5.3570315
## 148  4.8949288  5.4371964  5.1756045  4.9910429  5.2874284  5.5634326
## 149  4.7984882  5.2752762  4.9693068  4.8747170  5.0544543  5.3768739
## 150  4.6562861  4.8388111  4.9227157  4.6163516  4.7801605  4.9191398
## 151  4.9085595  4.6838019  5.3174377  4.7420584  4.9254978  4.6370117
## 152  4.8954077  4.7655840  5.3054685  4.7098543  4.9344534  4.7235986
## 153  6.3409166  6.2806017  6.6887542  6.1874846  6.4277905  6.1760747
## 154  4.9007070  4.8584402  4.9921228  4.7594507  4.6930418  4.9019232
## 155  6.2122864  6.1016679  6.4036759  6.1000573  6.1297854  6.1308097
## 156  6.8912688  6.8723071  6.5085650  6.7864315  6.3454789  6.9177496
## 157  5.5977377  5.7196167  5.2182614  5.4810016  5.0567283  5.8415344
## 158  5.6817956  4.9567685  6.0905831  5.3844646  5.4558948  4.4576941
## 159  4.5080975  3.9107481  5.0579650  4.1742229  4.3989500  3.5110640
## 160  5.3306938  4.8064925  5.7783064  5.0708711  5.2095728  4.7029062
## 161  6.1279199  5.6535278  6.4892209  5.8737616  5.9850120  5.3091739
## 162  6.6703093  5.8820613  7.0281758  6.3802512  6.4086279  5.3277917
## 163  7.8937702  7.2015482  8.2201581  7.6534430  7.6671704  6.8124436
## 164  8.1595671  7.4762616  8.4175902  7.9458968  7.8940911  7.1163756
## 165  4.0507266  3.6985847  4.6823862  3.8142437  4.1894797  3.2961703
## 166  4.4556033  4.0706733  4.5546257  4.1945986  4.0250096  3.7727139
## 167  6.8136465  6.0472068  7.1079557  6.5567444  6.5060107  5.6006888
## 168  4.3253305  4.1161691  4.3105426  4.1104740  3.9292872  3.7252928
## 169  4.2710357  3.8605694  4.5279058  4.0244912  3.9829644  3.5872998
## 170  4.1805184  3.7483880  4.5418947  3.9410804  3.9926959  3.4756468
## 171  3.8514636  3.7039532  4.0962330  3.6674927  3.6778719  3.5387956
## 172  3.9330403  3.6200898  4.4328653  3.6978616  3.9200181  3.3748970
## 173  2.8154550  2.6065176  3.6174062  2.5694442  3.1474455  1.7763983
## 174  3.3810682  2.6465529  4.0908564  3.0366205  3.4053281  1.6477295
## 175  3.2475042  2.7269753  3.9676771  2.9092131  3.4215718  1.3459793
## 176  4.4957315  3.8402714  4.9418687  4.1888165  4.4809167  2.3548774
## 177  3.4844467  3.0480471  4.0643107  3.2186135  3.6629137  1.5307719
## 178  3.6170021  2.8116384  4.3327325  3.2494194  3.6556051  1.5744152
## 179  4.0691949  3.2543298  4.6249147  3.7458164  3.9673339  2.2263249
## 180  4.7066350  3.8997850  5.1800999  4.3897066  4.5922522  2.7905789
## 181  5.0979899  4.2860296  5.4855075  4.8441215  4.8632475  3.6641197
## 182  3.9859240  3.4340546  4.5376154  3.6950620  4.0564275  2.1923997
## 183  4.7045790  3.7850101  5.2549766  4.3717086  4.5192711  3.0955590
## 184  3.9814322  3.0660101  4.6902387  3.6081654  3.9142321  2.3047593
## 185  2.7801228  2.4814730  3.5864897  2.5159928  3.0741675  1.6946191
## 186  3.1878554  2.7714887  3.7642157  2.9541029  3.3172995  1.6436885
## 187  6.1624026  5.3968118  6.4474284  5.9159274  5.9409646  4.5327444
## 188  5.2785745  4.7263198  5.6525381  5.0521880  5.2532035  3.5624475
## 189  5.3985996  4.8466165  5.7690039  5.1616444  5.3885305  3.6114574
## 190  5.7013147  5.0820827  6.0449108  5.4868808  5.6308235  4.0038228
## 191  6.0304926  5.4970126  6.3048099  5.8571234  5.9900751  4.4081024
## 192  5.5603601  5.0012986  5.9427604  5.3686509  5.5771660  3.9265158
## 193  6.1741741  5.5414473  6.5022330  5.9747708  6.1160464  4.4879151
## 194  6.1181127  5.6418166  6.4141891  5.9486543  6.1427719  4.5114286
## 195  5.8641766  5.3709941  6.1808388  5.6761766  5.8706893  4.2634855
## 196  7.8967158  7.2985773  8.1157028  7.7251976  7.7587006  6.3711789
## 197  7.2646605  6.7579532  7.5596990  7.1232195  7.2354800  5.8413773
## 198  6.8499399  6.4835361  7.0262664  6.7558382  6.7878696  5.6305173
## 199  7.1396769  6.6889234  7.4041356  7.0241925  7.1145466  5.8090780
##             37         38         39         40         41         42
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38   0.8735678                                                       
## 39   1.2780680  0.6243352                                            
## 40   4.1974105  3.8449661  3.7011002                                 
## 41   4.6851227  4.2964738  4.0948048  0.8510830                      
## 42   3.0618459  2.3885275  2.0836491  3.3931602  3.4788406           
## 43   2.6263737  1.8911401  1.6313090  3.4427789  3.7090611  0.8876224
## 44   2.5738067  1.8514851  1.5700007  3.4640280  3.7466208  0.9134614
## 45   1.6503699  1.2409068  1.3373524  3.6583292  4.0875575  1.8746120
## 46   1.5688941  1.1019857  1.2573337  3.8582391  4.3628251  2.2138325
## 47   1.6014756  1.2962120  1.3084754  3.9418915  4.4488365  2.3334703
## 48   1.9865979  2.4715369  2.7538300  4.7994268  5.3301923  3.8380425
## 49   3.4269216  3.9562478  4.1551637  6.1202410  6.7375355  5.4395750
## 50   1.7240064  1.8747440  2.1055728  4.3816739  4.9450424  3.2189054
## 51   2.3442324  2.1766698  2.2738181  3.3304212  3.8974818  2.6562733
## 52   2.3022023  2.2311983  2.4445525  3.2933285  3.8073634  2.7722360
## 53   3.0114750  2.4654292  2.3504962  2.6270368  2.9002449  1.4140908
## 54   2.7308567  2.2056047  2.1290352  2.8585715  3.3199191  1.8505824
## 55   4.1400933  4.0628480  4.1288755  3.1446651  3.7878973  4.7021883
## 56   5.7077093  5.3701289  5.2104766  2.0506326  1.8421016  4.4306886
## 57   5.0350774  4.7499243  4.7516374  2.1723370  2.5974563  4.3545040
## 58   5.8077759  5.5721469  5.5185886  2.4381013  2.5409197  4.9527930
## 59   2.8257975  2.3230261  2.3117494  2.8487737  3.2701931  2.2794592
## 60   2.1801980  1.8976648  2.0816433  3.1190345  3.6788328  2.7475858
## 61   2.2357152  2.2738378  2.5319535  3.6747204  4.2857823  3.4851597
## 62   2.4201710  2.7867079  3.1326469  4.2293306  4.8117116  4.1701936
## 63   2.4864360  2.3775502  2.5769464  3.1585557  3.5628526  2.9447645
## 64   2.9674582  2.6601902  2.6192617  2.9322219  3.2244044  2.4538631
## 65   3.8703396  3.6614800  3.5935111  3.4856163  3.5621925  3.0219266
## 66   4.5930948  4.2392765  4.1932726  1.6089047  2.1265528  3.7894165
## 67   4.2952364  4.0846128  4.1198825  2.3243993  3.0529928  4.2005072
## 68   2.3660045  1.7581451  1.7154117  3.2122140  3.6718852  1.9329177
## 69   2.0831505  1.7996581  1.9492783  3.7451370  4.3383370  2.7969315
## 70   2.1172972  1.6287223  1.7004980  3.2880517  3.7827462  2.1577193
## 71   2.6488368  1.9781813  1.7066186  3.5998951  3.8239755  1.1918587
## 72   2.1098353  1.5265133  1.3780802  3.7978173  4.1924811  1.8434828
## 73   2.5360741  1.8102988  1.6335944  3.6827251  3.9851680  1.4945217
## 74   2.5527396  1.8798500  1.6196038  3.6613875  3.9389029  1.3628489
## 75   2.6305592  2.0020908  1.7414252  3.8381382  4.0805959  1.7491241
## 76   1.7359412  1.5294587  1.6095859  3.9743109  4.3293299  2.3658974
## 77   1.5989618  1.9669076  2.2136332  4.4677696  4.8766402  3.3190705
## 78   1.5771422  1.4479722  1.5518054  4.0838597  4.4801740  2.5697887
## 79   1.6948864  1.6885048  1.7986180  4.1478612  4.5507964  2.7028306
## 80   1.7468386  1.3976114  1.5024250  4.0646938  4.4922021  2.4767769
## 81   2.5738700  2.1293292  1.9784653  2.2673036  2.4846012  1.6966207
## 82   2.0994980  2.1159431  2.2837261  2.9208120  3.2992189  2.7669961
## 83   2.1843753  1.6895713  1.6128450  2.3812653  2.8041783  1.8167679
## 84   1.8500106  1.5474886  1.6544576  2.6296749  3.1335420  2.2611308
## 85   1.4109969  1.1584379  1.1823829  3.5478547  3.9015042  1.9543196
## 86   1.7272163  1.5670766  1.5940272  3.5264974  3.7721509  2.0622718
## 87   1.1073881  0.9521111  0.9953423  3.7761154  4.2346979  2.3369665
## 88   0.9534773  0.9471173  1.2246366  3.7761027  4.1891492  2.4699374
## 89   2.2594887  2.5057561  2.7073260  4.2212708  4.4283764  3.2655992
## 90   2.3171440  2.2979445  2.2755181  3.7825382  3.8918432  2.5487566
## 91   1.2813436  1.5143158  1.7144052  3.9541955  4.3066524  2.7936479
## 92   1.3510685  1.6773917  1.9426708  4.0759456  4.4346474  3.0197709
## 93   2.1642623  2.1154428  2.1877223  3.2124479  3.5930389  2.7836990
## 94   2.4517239  2.0765537  1.9871052  2.9663531  3.3217812  2.3378274
## 95   2.0603499  2.3544804  2.5869803  3.7603988  4.2274165  3.5455925
## 96   1.8527549  1.8320453  1.8063398  3.6355145  3.8575594  2.3623984
## 97   1.0905830  1.4888372  1.7513494  4.0631542  4.5015309  3.0093014
## 98   4.0455667  4.0589451  3.9349055  4.4812571  4.2765743  3.6685390
## 99   4.1797281  3.9309561  3.6121895  4.0708484  3.7505591  2.9615735
## 100  2.9175823  2.8812234  2.7581522  3.8506625  3.8314993  2.7270173
## 101  2.0156083  2.3259724  2.4150479  4.4983772  4.7326698  3.6181466
## 102  1.9922143  2.1682767  2.2444887  4.3371351  4.5481595  3.3384078
## 103  3.7386253  4.1794522  4.3174030  5.9795484  6.2875859  5.2351853
## 104  1.5595274  2.1920666  2.4937371  4.9424183  5.3752316  4.1438024
## 105  1.6369227  2.2649786  2.5651834  4.9604230  5.3739402  4.1943341
## 106  1.9120830  2.6400905  2.9292024  5.3667925  5.8450569  4.7156562
## 107  1.9327462  2.6461481  2.8932522  5.3809815  5.8712477  4.7027387
## 108  1.6038532  2.2486831  2.5005073  4.9847750  5.4083892  4.2022288
## 109  1.9634765  2.5763046  2.8596649  5.0587945  5.4279262  4.3214695
## 110  1.7681886  2.4414672  2.7034623  5.0941899  5.5224970  4.3351704
## 111  1.3008877  1.5139362  1.5976559  4.4071830  4.7974236  3.2844384
## 112  2.0275261  2.3985835  2.5687013  4.6269260  4.9133860  3.6192669
## 113  1.9442755  2.6124101  2.8953161  5.2592255  5.7358851  4.4701548
## 114  2.0530950  2.7229346  2.9884001  5.2803338  5.7393426  4.4883940
## 115  1.7664866  2.2758223  2.5794568  4.8660870  5.2626757  3.9282579
## 116  1.8491415  2.5292544  2.8007940  5.1867590  5.6615535  4.3371998
## 117  1.5190800  1.9345377  2.1496469  4.6081874  5.0094817  3.5585865
## 118  1.6013523  2.0902907  2.4244986  4.7938519  5.2246606  3.8520350
## 119  1.6199982  2.1866065  2.3783862  4.9131044  5.3775998  3.9453648
## 120  1.4243256  1.8225320  2.0695816  4.7422748  5.2287482  3.6952957
## 121  3.1237118  3.3797959  3.4856031  5.6936127  6.0747382  4.6022917
## 122  3.2141260  3.5794866  3.7455321  5.8763420  6.2575874  4.8683646
## 123  3.4124236  3.8691548  4.0300245  6.1580916  6.5629724  5.2444349
## 124  3.8923172  4.4280535  4.5731223  6.7245169  7.1840714  5.8823600
## 125  3.4402495  3.9150854  4.1091575  6.2496307  6.6728942  5.3562546
## 126  3.2867225  3.6808232  3.8430028  5.9592215  6.3385847  5.0045261
## 127  4.0633422  4.6080819  4.7580091  6.9515579  7.4459296  6.1331396
## 128  3.3582307  3.8475852  4.0870787  6.4146040  6.8672656  5.6505145
## 129  3.4245549  3.8871978  4.0849667  6.2144702  6.5613950  5.4069122
## 130  3.4065507  3.8937782  4.1431667  6.4904278  6.9645622  5.7144381
## 131  3.3581830  3.7787257  3.9874579  6.0616481  6.3842027  5.2413351
## 132  3.2854145  3.6944148  3.9097364  6.0167344  6.3526915  5.1954177
## 133  3.3048134  3.6910365  3.8733729  5.9176761  6.2179910  5.1102009
## 134  3.2014729  3.6482868  3.8831681  6.1559212  6.5774421  5.3583656
## 135  3.5757979  4.1131548  4.3376406  6.5528631  6.9961471  5.7730992
## 136  3.3987198  3.8733983  4.0650471  6.2310225  6.5992435  5.4230011
## 137  3.2776212  3.7543950  3.9639934  6.2539502  6.6716170  5.4463218
## 138  3.4129012  3.8667665  4.0775928  6.1980099  6.5433460  5.3767620
## 139  3.6265103  4.1603902  4.3844627  6.6886791  7.1525566  5.9290118
## 140  3.4518596  3.9524486  4.1414925  6.3725292  6.7687150  5.5961993
## 141  3.7636073  4.2883004  4.4503555  6.7084590  7.1411632  5.9147219
## 142  4.8185586  5.3723066  5.5153051  7.8163157  8.3721927  7.2161674
## 143  6.5718806  6.9344725  7.0672998  8.8293194  9.2568036  8.1993182
## 144  5.2010899  5.6418576  5.7870754  7.8016782  8.2604259  7.0925004
## 145  5.5408518  5.9827488  6.1510889  8.2369863  8.7633916  7.5602981
## 146  5.7307699  6.2304985  6.3300665  8.1510178  8.5415381  7.3928687
## 147  5.2813504  5.7169612  5.8829255  7.7064748  8.0983493  6.9530452
## 148  5.4768474  5.9106251  6.0539966  8.1321094  8.6463378  7.4545187
## 149  5.2779137  5.7126167  5.8250726  7.8703031  8.3467138  7.1660889
## 150  4.8805706  5.2922869  5.4511412  7.4490867  7.8815792  6.6745625
## 151  4.6688635  5.0061849  5.1451405  6.9516046  7.2672855  6.1582965
## 152  4.7273818  5.0877209  5.2814085  7.1940274  7.5921224  6.4612271
## 153  6.1665311  6.3986978  6.5753166  8.2571484  8.6531386  7.5814543
## 154  4.8597282  5.2624984  5.4159951  7.2806612  7.6544731  6.5146723
## 155  6.1376085  6.4255360  6.5543618  8.0982919  8.4005281  7.3825602
## 156  6.8320723  7.1222638  7.2065233  8.6329171  8.9104728  7.8789580
## 157  5.7276620  6.1346736  6.3041407  8.0893229  8.5061050  7.3409994
## 158  4.5343456  4.7248674  4.7043084  5.8205294  5.8437690  5.0788257
## 159  3.6067235  3.9499391  4.1557914  5.8540075  6.1579960  5.0198583
## 160  4.7929934  5.0618897  5.2084292  6.7941075  7.0160382  5.9906174
## 161  5.3603095  5.5540137  5.6586957  6.9116817  7.1164509  6.2017807
## 162  5.4021019  5.4789697  5.3650782  6.0847240  5.9279133  5.4011979
## 163  6.8925373  6.9739262  6.8897652  7.4199595  7.2634413  6.8817344
## 164  7.1957761  7.2657170  7.1527517  7.5783130  7.3620746  7.0052748
## 165  3.3465184  3.6889304  3.8810674  5.7759653  6.1555471  4.8773044
## 166  3.7451587  4.1227219  4.2578934  5.9378194  6.2437311  5.0467847
## 167  5.6800684  5.7934443  5.6717178  6.3089355  6.1169202  5.6420164
## 168  3.6283683  3.9676511  4.0700682  5.8803057  6.2301768  4.9067113
## 169  3.6063731  4.0084634  4.1550642  5.8707608  6.1721415  4.9692832
## 170  3.5225547  3.9098128  4.0708297  5.8032860  6.1086333  4.8690664
## 171  3.5193300  3.9779996  4.1929699  6.1101174  6.5297923  5.2005189
## 172  3.4172816  3.8358918  4.0702250  5.9642858  6.3658822  5.0761124
## 173  1.7662843  2.3720601  2.6335491  4.8912624  5.3976893  4.1753187
## 174  1.8115546  2.2212405  2.4452467  4.3965765  4.7370863  3.4906701
## 175  1.3714148  1.6917672  1.9456882  4.2979494  4.7401805  3.2958128
## 176  2.3154319  1.9557050  1.7493367  3.6024976  3.7665662  1.9693130
## 177  1.4314712  1.3285439  1.3984538  3.8985752  4.3099157  2.5250897
## 178  1.7262533  1.9029115  2.1199894  4.0784845  4.4054867  3.0181122
## 179  2.3410425  2.4925684  2.5183147  4.0960157  4.2618739  3.0780619
## 180  2.8365305  2.7565439  2.5841368  3.8428973  3.8500667  2.7939755
## 181  3.7630017  3.8939259  3.7705077  4.5930410  4.4881142  3.8706563
## 182  2.1324720  2.2044660  2.0696218  3.9869133  4.2382559  3.0906248
## 183  3.2359290  3.4236029  3.4095698  4.4639065  4.4834466  3.8129906
## 184  2.4763284  2.7823517  2.9078083  4.3827018  4.5897399  3.7194496
## 185  1.6739316  2.2694912  2.4982603  4.6893741  5.1749231  4.0261501
## 186  1.5585066  1.8670473  1.8687388  4.0673887  4.4356125  3.1073134
## 187  4.5523080  4.4234819  4.1270109  4.5402835  4.2216800  3.7469421
## 188  3.5469911  3.3672036  3.2279063  2.4027672  2.5622573  3.1077418
## 189  3.5757783  3.2614516  3.1319422  2.1861735  2.4085174  2.8173088
## 190  4.0066366  3.7780170  3.5987088  2.4437454  2.3728712  3.1105411
## 191  4.3507132  3.9765553  3.7409464  2.3544931  2.2616806  2.9110781
## 192  3.9048940  3.5584757  3.4365554  2.2212435  2.3679765  2.8019737
## 193  4.4757209  4.1076797  3.9073089  2.4312457  2.2392467  2.9878194
## 194  4.4528741  4.0323582  3.8346623  1.5838340  1.6530074  2.9503516
## 195  4.2131793  3.8333070  3.6987432  1.5237703  1.7763464  2.9757759
## 196  6.3642559  6.1225503  5.8728417  3.3611090  2.8224192  5.0437005
## 197  5.8488140  5.6034046  5.4961845  3.0566790  2.9642591  4.6642360
## 198  5.5980791  5.4219711  5.3243700  3.0794948  3.1597461  4.6526562
## 199  5.8027241  5.5970197  5.4780759  3.1081328  3.0491487  4.7273310
##             43         44         45         46         47         48
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44   0.2733197                                                       
## 45   1.3804106  1.3009287                                            
## 46   1.5258416  1.4457536  0.7048007                                 
## 47   1.7325510  1.5823929  0.8628512  0.5765737                      
## 48   3.4799926  3.3540708  2.1320414  2.2873933  2.0495159           
## 49   4.9818033  4.8226112  3.7670774  3.6979452  3.3319549  1.9552306
## 50   2.6656173  2.5508278  1.4125661  1.3929076  1.1893861  1.1537503
## 51   2.2235973  2.1127564  1.3375224  1.5282156  1.4343145  2.0238261
## 52   2.4411424  2.3936641  1.4409522  1.8096384  1.8874243  1.9917875
## 53   1.3880445  1.3930188  1.6665525  2.0604096  2.2090577  3.3963995
## 54   1.3895288  1.3445887  1.3896911  1.5640044  1.6843420  3.0425466
## 55   4.4411206  4.3766386  4.0124831  4.0775953  4.0233397  4.1959998
## 56   4.6566657  4.6640311  4.8831673  5.2431568  5.2645913  5.8273040
## 57   4.2910209  4.2914560  4.2284635  4.4736568  4.5442132  4.9763905
## 58   5.0269410  5.0424488  5.0447566  5.3347999  5.3932379  5.7665404
## 59   2.0101522  2.0025600  1.9164472  2.2061971  2.3345930  3.2716414
## 60   2.3440695  2.2991183  1.6754228  1.8590179  1.9621712  2.5416982
## 61   3.0468644  2.9752052  2.0633736  2.2034654  2.1815967  2.0447665
## 62   3.8315735  3.7606565  2.6508080  2.8574556  2.8025032  1.7630215
## 63   2.8084421  2.7910359  2.0723515  2.5216482  2.6263519  2.6183634
## 64   2.4879949  2.4291096  2.1553363  2.6599481  2.6420124  3.0608260
## 65   3.2067151  3.1861913  2.9173903  3.5324318  3.5143856  3.5854330
## 66   3.7089786  3.7181786  3.8392682  3.9624851  4.0674293  4.8885074
## 67   3.9184502  3.8855216  3.7145922  3.7216441  3.7588817  4.3453569
## 68   1.3853910  1.3490450  1.3359757  1.4034956  1.5765214  3.0091858
## 69   2.1999386  2.0991477  1.4536378  1.3253685  1.3100885  2.2931502
## 70   1.6394660  1.5901616  1.1702386  1.2955010  1.4550548  2.6340064
## 71   1.0808584  1.0611542  1.7127745  1.8841906  1.9992088  3.5667248
## 72   1.3166889  1.2459375  1.3035799  1.2607838  1.3398381  2.9580943
## 73   1.0579184  1.0839398  1.6342248  1.6460226  1.8746938  3.5415358
## 74   1.0634820  1.0351752  1.6346479  1.7225672  1.8363945  3.4783959
## 75   1.5691645  1.5522220  2.0457759  2.0616782  2.1793305  3.7367039
## 76   2.1205760  2.0751633  1.5412476  1.7278860  1.7997784  2.5713550
## 77   3.0757211  3.0149723  2.0694162  2.2568047  2.2230419  1.9696669
## 78   2.2523365  2.1918179  1.6019938  1.6663470  1.7021351  2.4761405
## 79   2.4203319  2.3345751  1.5679828  1.7778377  1.7105530  2.1063972
## 80   2.0187831  1.9730580  1.5318923  1.4500922  1.5851987  2.7008830
## 81   1.8186503  1.8247264  1.8680722  2.2867160  2.3952384  3.3407276
## 82   2.6977002  2.6738073  1.9043242  2.3541669  2.4314391  2.4284166
## 83   1.5981847  1.5847734  1.4675984  1.7394755  1.8823633  3.0066514
## 84   1.9520815  1.9322957  1.3572502  1.6232047  1.7711189  2.5599628
## 85   1.7318168  1.6575645  0.8885072  1.3250026  1.3502586  2.1716103
## 86   2.0352455  2.0247648  1.4383606  1.9114407  2.0156008  2.5527688
## 87   1.8949826  1.7825903  0.9298010  0.9773747  0.8362141  1.9320920
## 88   2.1301340  2.0951345  1.2198718  1.3565854  1.4974582  2.1427567
## 89   3.3374398  3.3242250  2.5545031  2.9619491  3.0447118  2.7556599
## 90   2.7406653  2.7325649  2.3129114  2.7514493  2.8093898  3.0945574
## 91   2.6214452  2.5818620  1.7740498  1.9848130  2.0407789  2.2653225
## 92   2.8442743  2.8133229  1.9318538  2.1479900  2.2267132  2.2301897
## 93   2.6513079  2.6180798  2.1187239  2.3044625  2.3674909  2.8613439
## 94   2.1338955  2.1359857  2.1188480  2.1690584  2.3091144  3.4529474
## 95   3.3163540  3.2663327  2.4081950  2.5505644  2.5639114  2.3688328
## 96   2.3401010  2.3545625  1.8611525  2.2233105  2.3039180  2.8074648
## 97   2.7090474  2.6456027  1.6520744  1.7810185  1.7713382  1.7969808
## 98   4.1385635  4.1416213  3.9327288  4.4665547  4.4649939  4.4717377
## 99   3.5183540  3.5438518  3.8086809  4.2707519  4.2773182  4.9271704
## 100  3.0656046  3.0539114  2.7904327  3.2767257  3.2811854  3.5281010
## 101  3.5934715  3.5610971  2.9210197  3.1840405  3.1740835  3.0472434
## 102  3.3488907  3.3268014  2.7820567  3.0522995  3.0832783  3.1648142
## 103  5.0907395  5.1379601  4.5131549  4.6573001  4.6615489  4.3922310
## 104  3.8834796  3.8183103  2.9060771  2.9586696  2.9091178  2.4275402
## 105  3.9518971  3.8984873  3.0028697  3.0658058  3.0425914  2.5803482
## 106  4.3880768  4.3144640  3.3607576  3.3258941  3.2297931  2.5580354
## 107  4.3656987  4.2750105  3.3427284  3.2880930  3.1374162  2.4853883
## 108  3.9460153  3.8810302  3.0228088  3.0454637  2.9777366  2.5917605
## 109  4.1684106  4.1108045  3.2058100  3.3523758  3.3151884  2.6718104
## 110  4.1004549  4.0214726  3.0982922  3.1653979  3.0606028  2.4229424
## 111  3.0392983  2.9634523  2.3885853  2.3931265  2.3234728  2.7156517
## 112  3.5642470  3.5154706  2.7585504  2.9938845  2.9783721  2.7173876
## 113  4.1443160  4.0654063  3.0869531  3.0621173  2.9609800  2.2902713
## 114  4.2089906  4.1200772  3.1288561  3.1591678  3.0273000  2.2176014
## 115  3.7071101  3.6626639  2.7915908  2.8562936  2.8791706  2.5734504
## 116  4.0077458  3.9452852  2.9846454  2.9690670  2.8760628  2.3058269
## 117  3.3044040  3.2444375  2.4384623  2.4921132  2.4636472  2.4139357
## 118  3.5534917  3.5132816  2.6076123  2.6338266  2.6788044  2.4308670
## 119  3.5913267  3.5324283  2.6951562  2.6394788  2.5403329  2.4027481
## 120  3.2827464  3.2148173  2.4138579  2.2725937  2.2339936  2.3877547
## 121  4.3187583  4.2642459  3.6786573  3.6227672  3.5686844  3.5951722
## 122  4.6161964  4.5645424  3.8596448  3.8541211  3.8040267  3.5378976
## 123  4.9792186  4.9087336  4.1355576  4.1246891  4.0112055  3.5209730
## 124  5.5865892  5.4798745  4.6621758  4.6024264  4.3824123  3.6722256
## 125  5.0707923  5.0025483  4.1988242  4.1671293  4.0696564  3.5381356
## 126  4.7525173  4.6987045  3.9775702  3.9727015  3.9128050  3.5859285
## 127  5.7896105  5.6804820  4.8636042  4.7482189  4.5177328  3.8323285
## 128  5.3327414  5.2665432  4.4777176  4.3937948  4.3225472  3.8380700
## 129  5.2575079  5.1906355  4.4438475  4.5088422  4.4327816  3.8818456
## 130  5.3796252  5.3041866  4.5032905  4.3995464  4.3139775  3.8044884
## 131  5.1073671  5.0578912  4.3269348  4.4230355  4.3912580  3.8967385
## 132  5.0320570  4.9862680  4.2535689  4.3327784  4.3119024  3.8518932
## 133  4.9695244  4.9376832  4.2404957  4.3538583  4.3447264  3.9376641
## 134  5.0684997  5.0144089  4.2354976  4.2118122  4.1666011  3.7073814
## 135  5.4667455  5.4314877  4.6294900  4.6025798  4.5309872  3.9810210
## 136  5.2468712  5.1724290  4.4080021  4.4613320  4.3610437  3.7751603
## 137  5.1810197  5.1157334  4.3526258  4.3230077  4.2407819  3.7685352
## 138  5.2323394  5.1691909  4.4227810  4.4909277  4.4290671  3.8892887
## 139  5.6387475  5.5463048  4.7330156  4.6559555  4.5166793  3.8781680
## 140  5.3784541  5.2988007  4.5306742  4.5306530  4.4150159  3.8430335
## 141  5.6879299  5.5769492  4.8095493  4.7730927  4.5732985  3.9238997
## 142  6.7967534  6.6685913  5.8728891  5.6672288  5.3994188  4.7063925
## 143  7.9084727  7.8245170  7.2119146  7.0962501  6.9584366  6.5092160
## 144  6.7719637  6.6771225  5.9687467  5.8486161  5.6804085  5.1359349
## 145  7.1507639  7.0510092  6.3298038  6.1208510  5.9481789  5.4341578
## 146  7.1836946  7.1204243  6.4487118  6.4417034  6.2525742  5.6507580
## 147  6.6746782  6.6693215  6.0119474  5.9724147  5.9307385  5.5367078
## 148  7.0494915  6.9507254  6.2496563  6.0515642  5.8687190  5.3843413
## 149  6.8012146  6.7114989  6.0351257  5.8839465  5.6976614  5.2374581
## 150  6.3740747  6.3059886  5.6259661  5.5307170  5.4185514  4.9832241
## 151  5.9780690  5.9402380  5.3300076  5.3535769  5.3150522  4.9713994
## 152  6.1436401  6.1257534  5.4661281  5.3881183  5.3930482  5.0869296
## 153  7.2488515  7.2387101  6.7293113  6.5934832  6.6278033  6.5231339
## 154  6.2492854  6.2313869  5.5826216  5.5543866  5.5126320  5.1492408
## 155  7.2209206  7.1901432  6.6644295  6.6752455  6.6377919  6.3289472
## 156  7.7294585  7.7394623  7.3056886  7.3279902  7.2946466  7.1148979
## 157  7.0134853  7.0276701  6.4102928  6.3303534  6.3118754  6.0180167
## 158  5.1547252  5.1860037  4.7848461  5.0656708  5.1035529  4.9934828
## 159  4.8185914  4.8330814  4.1308384  4.2033189  4.2921904  4.0194386
## 160  5.9098404  5.9065380  5.3570819  5.4692103  5.5089351  5.2340246
## 161  6.0918073  6.1118264  5.6633267  5.7475170  5.8138755  5.7173542
## 162  5.6322486  5.6769681  5.4836608  5.8361368  5.8741116  5.9102043
## 163  7.1134102  7.1415850  6.9571728  7.2791158  7.2991885  7.2374451
## 164  7.3278793  7.3426563  7.2034904  7.5699965  7.5587320  7.4798848
## 165  4.5979120  4.5660442  3.8226703  3.8288370  3.8360092  3.5387451
## 166  4.8453206  4.8687786  4.2028110  4.3019859  4.3248010  4.0631777
## 167  5.9434722  5.9703055  5.7545552  6.1528648  6.1497318  6.0591388
## 168  4.6405981  4.6546341  4.0439785  4.0718328  4.0637343  3.9734875
## 169  4.8109100  4.8047610  4.0951446  4.2146854  4.2063362  3.8274458
## 170  4.7255666  4.7047213  3.9800288  4.1064418  4.0923357  3.6835678
## 171  4.9095912  4.8815729  4.0710589  4.0712255  4.0350469  3.5584060
## 172  4.7940626  4.7683276  3.9577277  3.9674998  3.9738270  3.5284582
## 173  3.7454134  3.6864866  2.6929238  2.6062503  2.5466065  2.1072021
## 174  3.3324675  3.3007145  2.4333411  2.6270902  2.6641931  2.4195800
## 175  2.9182017  2.8895790  2.0549160  2.0119761  2.0936704  2.3479221
## 176  1.9770654  1.9986797  2.0469077  2.2531784  2.3730365  3.4623935
## 177  2.1501078  2.0981851  1.4821434  1.4804132  1.5328115  2.4265960
## 178  2.8317831  2.8306533  2.0484401  2.2703728  2.4059046  2.5413009
## 179  3.1367045  3.1283330  2.5651822  2.9198941  2.9573846  3.0264095
## 180  2.9851333  3.0071390  2.8328547  3.2016809  3.2511597  3.7324060
## 181  4.2129420  4.1991437  3.8686045  4.3406882  4.2929116  4.1838507
## 182  2.8960615  2.8924262  2.4694873  2.6170667  2.6192432  3.1182847
## 183  3.9727270  3.9905583  3.4960186  3.9060641  3.9456222  3.7986862
## 184  3.6616195  3.6758746  2.9439643  3.2554970  3.3345252  3.0807923
## 185  3.6050064  3.5582227  2.5604106  2.5404551  2.4879418  2.0559395
## 186  2.8464828  2.7888074  2.0229902  2.1855798  2.0809108  2.2178134
## 187  4.2041593  4.2298319  4.3441911  4.8019187  4.7846011  5.2036937
## 188  3.1966446  3.1951784  3.1576224  3.4077931  3.4389761  4.0850227
## 189  2.8402674  2.8682434  2.9753851  3.1854195  3.2870142  4.1787328
## 190  3.3730430  3.3785297  3.4560348  3.8157627  3.8408739  4.4462744
## 191  3.1361207  3.1634153  3.4710238  3.8336164  3.8698276  4.7128309
## 192  2.9035491  2.9228333  3.0308500  3.3682000  3.4490186  4.2046895
## 193  3.2967384  3.3321126  3.6081802  4.0132631  4.0804623  4.8373334
## 194  3.1040532  3.1159121  3.4900253  3.7478468  3.8056258  4.7978108
## 195  3.0299448  3.0573632  3.2896064  3.5322229  3.6249679  4.5429965
## 196  5.4258877  5.4529090  5.7175934  6.1097648  6.1111478  6.6298949
## 197  4.8734898  4.8816440  4.9800274  5.3132808  5.3481881  5.7908156
## 198  4.7849765  4.7736762  4.7716157  5.0774223  5.0577688  5.4083410
## 199  4.9207333  4.9157916  4.9663143  5.3048120  5.3018828  5.6689020
##             49         50         51         52         53         54
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50   2.4443771                                                       
## 51   3.3643567  1.4121752                                            
## 52   3.6176839  1.6413436  0.8656335                                 
## 53   4.9890515  2.7820097  1.7358880  1.7639419                      
## 54   4.4414407  2.2397661  1.1848925  1.5270416  0.8706569           
## 55   4.8857736  3.9479080  3.3695788  3.5064222  3.8966879  3.6359969
## 56   7.0561633  5.5149831  4.3344674  4.2573652  3.5681837  3.9337853
## 57   6.0820653  4.6104338  3.4040490  3.3481196  3.1558749  3.2200346
## 58   6.9107661  5.5042480  4.2463592  4.0937369  3.7807059  4.0106067
## 59   4.6919899  2.6179662  1.9385819  2.0017432  1.6678452  1.5853889
## 60   3.9408714  1.9844454  1.5728527  1.5859886  2.0777277  1.7749541
## 61   3.2226902  1.6949286  1.6721232  1.6608333  2.7576194  2.3489270
## 62   2.9184444  2.0503438  2.2811105  2.0217627  3.4581122  3.1712844
## 63   4.2488828  2.4482718  2.0543938  1.6108933  2.2460261  2.3168837
## 64   4.5532753  2.7482403  2.0877556  1.9983721  1.8776407  2.0656734
## 65   5.0690606  3.4189456  2.8331054  2.5232225  2.4427923  2.8087487
## 66   6.0823639  4.4267608  3.1529196  3.2017893  2.6843671  2.7432964
## 67   5.2467155  3.9162465  2.7557907  2.9308113  3.0166910  2.7425494
## 68   4.3962301  2.1732951  1.7080206  1.9731485  1.6148530  1.2602049
## 69   3.4398805  1.4697930  1.4052361  1.8240590  2.3296074  1.7363888
## 70   4.0691054  1.8570747  1.4807306  1.6696224  1.7165382  1.3437941
## 71   5.0608953  2.8965251  2.6097453  2.7994994  1.9161771  2.0092872
## 72   4.3121188  2.1838177  2.1591563  2.4568709  2.1307706  1.8613862
## 73   4.9989328  2.7631125  2.5500404  2.7447261  2.0020699  1.9330284
## 74   4.9131653  2.7547703  2.5173702  2.7620658  1.9799871  1.9486213
## 75   5.1517538  3.0876631  2.8819320  3.0761084  2.3403174  2.3521410
## 76   4.1341662  2.2099850  2.3254121  2.2892387  2.4507362  2.3853895
## 77   3.4867797  2.0932241  2.5710738  2.3791136  3.1946341  3.0700945
## 78   3.9484035  2.1079351  2.3446425  2.3680895  2.6400515  2.4824983
## 79   3.5925500  1.8429248  2.1349646  2.1413771  2.6325251  2.4632770
## 80   4.0967564  2.1049036  2.2891540  2.3968154  2.5331545  2.2780611
## 81   5.0027539  2.9207886  2.2538736  2.1091376  1.4086513  1.8149719
## 82   4.1778398  2.3955748  2.0495590  1.5510512  2.1837297  2.3307848
## 83   4.5839632  2.4401084  1.8022391  1.7947265  1.3691064  1.4157173
## 84   4.1662566  2.0751355  1.5782275  1.4393896  1.6764544  1.5745710
## 85   3.8933315  1.7846703  1.8115227  1.7278142  1.9333787  1.9090013
## 86   4.3592242  2.3358662  2.3003920  1.9883216  2.0950114  2.2965265
## 87   3.4236553  1.3670691  1.6934263  1.8615389  2.2777604  1.9662641
## 88   3.8319617  1.8158177  2.0905553  1.9236380  2.4090836  2.2864461
## 89   4.5501495  3.0413624  3.1142177  2.5894357  3.1429735  3.3967120
## 90   4.8597258  3.1090340  3.0070274  2.6367627  2.6546150  3.0069563
## 91   3.9564800  2.2437251  2.4464501  2.1854762  2.7217750  2.7220888
## 92   3.9404246  2.3009586  2.5539453  2.2127582  2.8871833  2.8912541
## 93   4.3993949  2.6832399  2.4305200  2.2631787  2.5003832  2.5311458
## 94   4.9129557  2.9547381  2.5563455  2.5736356  2.2293738  2.2324550
## 95   3.7996246  2.4702886  2.5225053  2.2558526  3.1102829  3.0037250
## 96   4.5234206  2.6477048  2.6269978  2.3373999  2.4370117  2.6202263
## 97   3.4247124  1.7788639  2.1869272  1.9997381  2.8192294  2.6573051
## 98   6.1207301  4.6624821  4.4657289  4.0319259  3.8496507  4.4073537
## 99   6.5302910  4.7821259  4.4409204  4.2068368  3.4468365  4.0335776
## 100  5.2307106  3.5808893  3.4174163  3.0659729  2.9139158  3.3609910
## 101  4.4999318  3.2149892  3.6265548  3.3397879  3.7847293  3.8819752
## 102  4.7005986  3.2438994  3.5635146  3.2842777  3.5750946  3.7180589
## 103  5.3471265  4.5997188  4.9780333  4.7934155  5.3494616  5.3106253
## 104  3.5844357  2.7073421  3.4393984  3.2644203  4.1343854  3.9749176
## 105  3.7704120  2.8617407  3.5668622  3.3506075  4.1982861  4.0694230
## 106  3.3422712  2.9054011  3.7770754  3.6519817  4.6570678  4.4075952
## 107  3.1373714  2.8226308  3.7174401  3.6680812  4.6559471  4.3724553
## 108  3.6752453  2.8482890  3.5764068  3.4349496  4.2441131  4.0818513
## 109  3.9134006  3.1036205  3.7417996  3.4645659  4.3221513  4.2713365
## 110  3.4634392  2.8168390  3.5689992  3.4163945  4.3240950  4.1636602
## 111  3.9525384  2.5962459  3.1163848  3.1351015  3.5151344  3.3695208
## 112  4.2058877  2.9863836  3.2506989  2.9509852  3.5633274  3.6259342
## 113  3.1922013  2.6457322  3.3276644  3.2006808  4.2574456  4.0002286
## 114  3.1338057  2.6815021  3.3373279  3.1985732  4.2710721  4.0466872
## 115  3.9199462  2.8122136  3.2459311  2.9953602  3.8059503  3.7117098
## 116  3.2623898  2.6145910  3.2553566  3.1438558  4.1544317  3.8995776
## 117  3.7428361  2.4854526  2.9045074  2.7627076  3.4643440  3.3235031
## 118  3.7626724  2.5574414  3.0434740  2.8066914  3.6731766  3.5136502
## 119  3.4099811  2.4747805  3.0467353  3.0264301  3.8399381  3.5658378
## 120  3.4766612  2.2648616  2.8127380  2.8255060  3.5711951  3.2576480
## 121  4.4023628  3.5850527  4.1975903  4.1806003  4.7263500  4.5266922
## 122  4.3512812  3.6952959  4.3400715  4.2420002  4.9331709  4.7649096
## 123  4.0965330  3.7897996  4.5164489  4.4466071  5.2619128  5.0512660
## 124  3.7187795  4.0644416  4.8735554  4.9242383  5.8590951  5.5578847
## 125  4.0869405  3.8214682  4.5694380  4.4894433  5.3508668  5.1250022
## 126  4.3515000  3.7726507  4.4426736  4.3343124  5.0573884  4.8866769
## 127  3.6763730  4.1899952  5.0354017  5.1362097  6.0977321  5.7402436
## 128  4.2998175  4.0821817  4.8872775  4.8227969  5.6797680  5.4274080
## 129  4.6452548  4.2586458  4.9173304  4.7603958  5.5032750  5.4134257
## 130  4.1784522  4.0543010  4.8749841  4.8425667  5.7261676  5.4457964
## 131  4.8077331  4.2293733  4.8462340  4.6349704  5.3380143  5.2876893
## 132  4.7565914  4.1412390  4.7755659  4.5691646  5.2795951  5.2079922
## 133  4.9118921  4.1915503  4.7953032  4.5585162  5.2139213  5.1767640
## 134  4.3504761  3.9218954  4.6814803  4.5665659  5.3851877  5.1784053
## 135  4.4391324  4.2563313  5.0137849  4.9345224  5.8030312  5.5647020
## 136  4.4468416  4.1496159  4.8425245  4.7182268  5.4975712  5.3715187
## 137  4.3423662  4.0362722  4.7899016  4.7116079  5.5109542  5.3073752
## 138  4.6941124  4.2642921  4.9076699  4.7391569  5.4747236  5.3948710
## 139  4.1323463  4.2453720  5.0596764  5.0480809  5.9526380  5.6877173
## 140  4.3749471  4.2011353  4.9443451  4.8608209  5.6680832  5.4934731
## 141  4.1309170  4.3490454  5.1144178  5.1457545  5.9854023  5.7514523
## 142  3.9879607  5.0085433  5.9538145  6.1493648  7.1630970  6.7013276
## 143  6.3746998  6.7294090  7.1743883  7.2406139  8.0110096  7.7118225
## 144  5.0105768  5.4039933  5.9337514  6.0016909  6.8823252  6.5521101
## 145  5.0323877  5.6392326  6.2367018  6.3776239  7.3188636  6.8890111
## 146  5.6419782  6.0320796  6.4424504  6.4863284  7.2753419  7.0449574
## 147  5.8833780  5.7419093  6.1297314  6.0544502  6.8055993  6.5893296
## 148  4.9925370  5.5678411  6.1596707  6.3070682  7.2219594  6.7952213
## 149  4.9842145  5.4282470  5.9800558  6.1038430  6.9644400  6.5828641
## 150  5.1365075  5.2066884  5.6679883  5.6816882  6.4904360  6.2102952
## 151  5.5946737  5.1820334  5.5079520  5.3663204  6.0160924  5.9045205
## 152  5.5570652  5.1969904  5.6193451  5.5005175  6.2593759  6.0319915
## 153  6.8680354  6.5155892  6.8556067  6.8074980  7.4090165  7.1605619
## 154  5.5874332  5.3319419  5.7208938  5.6262680  6.3574101  6.1594827
## 155  6.7836423  6.5237417  6.7868167  6.6932115  7.2613788  7.1496064
## 156  7.5617490  7.2585657  7.4522823  7.4006825  7.8447740  7.7425632
## 157  6.2917772  6.1410355  6.5158233  6.4773768  7.1966939  6.9374786
## 158  6.2541730  5.1171377  5.1826885  4.7887550  5.0372329  5.2605912
## 159  5.1281266  4.1693977  4.4502109  4.1122962  4.8113850  4.7701628
## 160  6.1770924  5.4355356  5.6377500  5.3657957  5.8798979  5.9113934
## 161  6.6387874  5.7905259  5.9362561  5.6878883  6.0897125  6.1069361
## 162  7.2422571  5.9867053  5.9202402  5.5192523  5.4708995  5.8355021
## 163  8.3908816  7.3664226  7.3022787  6.9466897  6.9300592  7.2642642
## 164  8.6532170  7.6611215  7.5396731  7.1996329  7.1034264  7.4982410
## 165  4.4375918  3.6569902  4.0172752  3.8212879  4.6154703  4.4462467
## 166  5.0425976  4.2072096  4.4652009  4.2198277  4.8789445  4.8058547
## 167  7.3685059  6.2369228  6.1542378  5.7523998  5.7225872  6.1267767
## 168  4.8288161  4.0095517  4.2753724  4.1559798  4.7629029  4.6031433
## 169  4.8308177  4.0730051  4.3427380  4.0872643  4.7936196  4.7451894
## 170  4.7183355  3.9571361  4.2145837  3.9589235  4.6786742  4.6386740
## 171  4.2812760  3.8016663  4.1955427  4.0534867  4.9481429  4.7378153
## 172  4.3850353  3.7420854  4.1255367  3.9165498  4.8019978  4.6250656
## 173  3.0887117  2.2039437  2.8570595  2.7231777  3.8304849  3.4919461
## 174  3.9881418  2.6185915  2.8490437  2.4782080  3.2568765  3.2561734
## 175  3.7661385  2.1807727  2.4999267  2.3242650  3.0558934  2.8418290
## 176  5.0642996  3.0571236  2.7776637  2.6815007  2.1991087  2.4120648
## 177  3.9042519  1.9975514  2.0324139  2.0459021  2.3669634  2.1576709
## 178  4.2199761  2.4867102  2.5743635  2.1745685  2.7696252  2.8003582
## 179  4.6790646  3.1110984  3.0866681  2.6920408  2.9936992  3.2230438
## 180  5.3511277  3.6117208  3.5225131  3.2124894  3.0106300  3.3555337
## 181  5.7057763  4.4224878  4.3680845  3.9710291  4.0026723  4.4290801
## 182  4.4817254  2.8584284  3.0776192  2.9063419  3.1237629  3.1033232
## 183  5.3757100  3.9760667  4.0398028  3.5495545  3.8116586  4.1371764
## 184  4.6541774  3.2344509  3.4730741  2.9658832  3.5704032  3.7137314
## 185  3.1395019  2.1026566  2.8418224  2.6600202  3.7358077  3.4286157
## 186  3.6067606  2.1152369  2.5005717  2.3745837  2.9907591  2.8503115
## 187  6.7077699  5.1393723  4.9048375  4.6171647  4.0907404  4.6107778
## 188  5.4949762  3.8436585  2.9505311  2.8019261  2.4300058  2.7023894
## 189  5.6142672  3.7742732  2.7463237  2.6559070  2.0244005  2.2834739
## 190  5.9205918  4.2376398  3.2856875  3.0873487  2.4871667  2.9482677
## 191  6.1185148  4.2974463  3.2020093  3.1304916  2.1753862  2.6231115
## 192  5.6547218  3.8075234  2.6420474  2.5129356  1.7852925  2.1662834
## 193  6.3319192  4.4871960  3.3989834  3.2272988  2.2766493  2.8376896
## 194  6.1544305  4.3290752  3.0897624  3.1304530  2.0863479  2.4457421
## 195  5.9156085  4.0781799  2.8335155  2.8183247  1.9673592  2.2560720
## 196  7.9381406  6.4414858  5.4020406  5.2082774  4.4659926  4.9760270
## 197  7.0361593  5.5761622  4.3142406  4.1616241  3.6413097  4.0102804
## 198  6.5157391  5.2296684  3.9662093  3.8979038  3.5739759  3.8141041
## 199  6.8446490  5.4864115  4.2514491  4.1206728  3.6964057  4.0239051
##             55         56         57         58         59         60
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56   3.8841901                                                       
## 57   2.7962673  1.9240733                                            
## 58   4.1092199  1.7108839  1.7009091                                 
## 59   2.9665131  3.7061104  3.0892422  4.1898919                      
## 60   2.7143038  4.1940470  3.3429792  4.4481588  0.9780989           
## 61   2.6927074  4.6302941  3.6428673  4.7452081  1.7790662  0.9262595
## 62   3.0943328  5.1083488  4.1388946  5.1000588  2.6956024  1.8519933
## 63   3.0479881  3.9699009  3.3422332  4.2562752  1.4744351  1.1503706
## 64   3.0615529  3.4779908  3.1412448  4.0749531  1.0979857  1.4230832
## 65   4.1291930  3.4643352  3.4320642  4.0491992  2.4216206  2.7543393
## 66   3.1383641  2.4416136  1.5947571  1.9887988  3.0919164  3.3006421
## 67   2.6293992  3.2317161  1.8843462  2.5981808  3.1506840  3.0558737
## 68   3.2973468  4.4161976  3.6743562  4.7278046  1.2629216  1.3816631
## 69   3.0689450  4.9359411  3.9340774  5.0741652  1.7846653  1.2974317
## 70   3.1680911  4.4811438  3.6598898  4.7246800  1.2731080  1.1193495
## 71   4.2791112  4.8309347  4.5614367  5.3520334  2.1176894  2.4091198
## 72   3.9697451  5.1204725  4.5780568  5.4855207  2.0365239  2.0168677
## 73   4.2337657  5.0048276  4.5748914  5.4332099  2.0744838  2.2880588
## 74   4.2107730  4.9307234  4.5781579  5.4116935  2.0960229  2.3329986
## 75   4.4385015  5.2259248  4.8879036  5.6025554  2.6083371  2.7530507
## 76   4.0497379  5.3112705  4.7603291  5.5085043  2.4862047  2.2086102
## 77   4.1687440  5.7576686  5.1169781  5.8121797  3.1164273  2.5484103
## 78   4.0562139  5.4891699  4.8918872  5.6476447  2.6452018  2.2766815
## 79   3.8976104  5.3810707  4.7562526  5.5472123  2.5303598  2.1267802
## 80   4.0143162  5.4904964  4.8121220  5.6450955  2.4734322  2.1684512
## 81   3.4769443  3.5056991  3.3640545  4.0126352  1.6461674  1.8896984
## 82   3.2894956  4.0455130  3.5523550  4.2369131  2.0720451  1.6873481
## 83   3.1619785  3.7771192  3.3142647  4.1417577  1.3338655  1.3826382
## 84   3.0090745  4.0071614  3.3596692  4.2283191  1.4435885  1.0992805
## 85   4.0525008  4.8225652  4.3635338  5.0829184  2.1557203  1.8825691
## 86   4.3314358  4.7685889  4.4679175  5.0436659  2.4366481  2.2521206
## 87   3.9738649  5.1511330  4.5506444  5.3401255  2.3457567  1.9078021
## 88   4.2016532  5.2324097  4.6645337  5.3578830  2.5696553  2.1013886
## 89   4.9350665  5.3867263  5.0548139  5.4369195  3.5461220  3.1768029
## 90   4.8907735  4.9772079  4.8633508  5.1956265  3.2433589  3.0951849
## 91   4.5212404  5.3792948  4.8786502  5.4181717  3.0885575  2.6334363
## 92   4.5780583  5.4791865  4.9439864  5.4754441  3.2102223  2.7089073
## 93   3.8473175  4.6760315  4.2736668  4.7379102  2.7676428  2.4405394
## 94   3.9522288  4.5576252  4.2219941  4.7151612  2.5976469  2.5148713
## 95   3.8631564  5.1449403  4.5501827  5.0467653  3.1770760  2.5872264
## 96   4.5733274  4.9625026  4.6932760  5.1548659  2.9151185  2.7154070
## 97   4.2671141  5.4597230  4.8188844  5.4721304  3.0098502  2.4276627
## 98   5.8838689  5.1560084  5.5772462  5.5750052  4.4464616  4.4904110
## 99   5.8857600  4.8168452  5.4338548  5.4342744  4.1835184  4.4678335
## 100  5.1003205  4.8604574  4.9858338  5.2135624  3.5222509  3.4887194
## 101  4.5648237  5.8058569  5.5561262  6.1512492  3.5358995  3.1286500
## 102  4.5274249  5.6717145  5.4419936  6.0548803  3.3540800  3.0130621
## 103  5.6770244  7.1513100  6.6913872  7.3104779  5.0316249  4.6515319
## 104  4.3527671  6.3537282  5.7436343  6.5192559  3.7003416  3.0004168
## 105  4.4696198  6.3905408  5.8123003  6.5486105  3.8009585  3.1183265
## 106  4.6080033  6.8061542  6.1389818  6.8945037  4.2151513  3.4493315
## 107  4.5458894  6.8058990  6.1394055  6.9153632  4.2015002  3.4386351
## 108  4.4764543  6.4471818  5.8833464  6.6180988  3.8604738  3.1803430
## 109  4.6161930  6.4051012  5.8925417  6.5765256  3.9752797  3.3178763
## 110  4.4491076  6.4691073  5.8858638  6.6341932  3.9116114  3.2047003
## 111  4.1302886  5.9054159  5.4273756  6.2342990  3.1321463  2.6359045
## 112  4.8273894  5.9389811  5.4891420  5.9197454  3.7685793  3.2983795
## 113  4.8156209  6.6667226  5.9100909  6.4861033  4.2213767  3.4982053
## 114  4.8170295  6.6255084  5.9008699  6.4632101  4.2434471  3.5289207
## 115  4.8084992  6.3127695  5.6567065  6.1838532  3.9041258  3.2914524
## 116  4.7693676  6.5994875  5.8422040  6.4301215  4.1176813  3.4228424
## 117  4.5729301  6.0488614  5.4209920  5.9807303  3.5616521  3.0017194
## 118  4.6575457  6.2424074  5.5159652  6.0965051  3.7095777  3.0791780
## 119  4.6418258  6.3796292  5.6702326  6.2671333  3.8418263  3.2236068
## 120  4.4901816  6.2575354  5.4865641  6.1469566  3.5688976  2.9501512
## 121  5.7135843  7.1003771  6.6522584  7.1568380  4.7440755  4.2849147
## 122  5.8158171  7.2421083  6.7707870  7.2551733  4.9352047  4.4190773
## 123  5.9300612  7.4848301  6.9927021  7.4730652  5.2245358  4.6544722
## 124  6.1681277  8.0008490  7.4377238  7.9621697  5.7582898  5.1215122
## 125  5.9676282  7.5951529  7.0550322  7.5533599  5.2962789  4.6972746
## 126  5.8936743  7.3245572  6.8653589  7.3275633  5.0592837  4.5289150
## 127  6.2849706  8.2571441  7.6323215  8.1903401  5.9638875  5.3028257
## 128  5.5442881  7.8405552  7.1661140  7.8853857  5.2664543  4.6129226
## 129  5.6006277  7.5361303  7.0484391  7.6661570  5.1941114  4.6231521
## 130  5.5197454  7.9057676  7.1875722  7.9418280  5.2895845  4.6184594
## 131  5.5481480  7.3698044  6.9017241  7.5097982  5.0304486  4.4952553
## 132  5.4826640  7.3388090  6.8436982  7.4710993  4.9480052  4.4100108
## 133  5.5114161  7.2196139  6.7932805  7.3771097  4.9014901  4.4116663
## 134  5.3678622  7.5279624  6.8927737  7.6069910  4.9587374  4.3523310
## 135  5.6478256  7.8956029  7.2187605  7.9369223  5.3589763  4.7499633
## 136  5.5193001  7.5345676  7.0172396  7.6626691  5.1530785  4.5691638
## 137  5.4668464  7.6413707  7.0362119  7.7309525  5.1216690  4.5091263
## 138  5.5945350  7.5223759  7.0258675  7.6497272  5.1671972  4.5986482
## 139  5.6786441  8.0650162  7.3864378  8.1112581  5.5488104  4.8676642
## 140  5.6053146  7.7266707  7.1765789  7.8288362  5.3187540  4.7030710
## 141  5.7270819  8.0264942  7.4361025  8.1296353  5.6228311  4.9791380
## 142  6.4196968  9.1427785  8.3628598  9.1262963  6.6877460  5.9663178
## 143  8.4360126  9.9694999  9.2445818  9.5613233  8.1308896  7.6086777
## 144  7.4140030  9.0422697  8.2833307  8.6083631  7.0333692  6.4476957
## 145  7.6342558  9.5235254  8.6364498  9.0496045  7.3876649  6.7569891
## 146  7.8373532  9.2604216  8.6297404  8.8871373  7.4513947  6.9470921
## 147  7.6120248  8.9392329  8.2292267  8.4884884  6.9913516  6.5121342
## 148  7.5735680  9.4042890  8.5533863  8.9472105  7.2996426  6.6899542
## 149  7.4422161  9.1180121  8.3477105  8.6907055  7.0835532  6.5141763
## 150  7.2244663  8.7175405  7.9748814  8.2827113  6.6864209  6.1409764
## 151  7.1433158  8.1718095  7.6114984  7.7798111  6.3402237  5.8969810
## 152  7.2151612  8.5072449  7.7768819  8.0317152  6.4811454  5.9807951
## 153  8.2093758  9.5028100  8.7409456  9.0494885  7.5681734  7.1397821
## 154  7.2933576  8.5294793  7.8643064  8.0936248  6.5898818  6.1164758
## 155  8.1612357  9.1812811  8.6213875  8.8165019  7.5093053  7.1184298
## 156  8.7299246  9.6623438  9.1457631  9.3362640  8.0689972  7.7624840
## 157  7.9184621  9.3200286  8.5434167  8.8544381  7.3253554  6.8691119
## 158  6.8899062  6.8418367  6.8142223  6.6185431  5.6924662  5.5163143
## 159  6.3045731  7.1775552  6.6054022  6.7348904  5.2979772  4.8487647
## 160  7.2757463  7.9560483  7.5099703  7.5864096  6.2855209  5.9290393
## 161  7.4410631  8.0123503  7.6110186  7.6757171  6.5232907  6.2333695
## 162  7.4932613  6.8905686  7.1786989  6.8154882  6.1972733  6.1855349
## 163  8.6285875  8.0356917  8.3330831  7.9858670  7.5360714  7.5216558
## 164  8.8356451  8.0760768  8.4953992  8.1054621  7.7472908  7.7733450
## 165  5.9655446  7.0891942  6.4151867  6.6546670  5.0445086  4.5449472
## 166  6.2991835  7.1763721  6.6287596  6.7760008  5.3221757  4.9240507
## 167  7.6787715  6.9959143  7.3663088  6.9647229  6.4498386  6.4384980
## 168  6.1515732  7.1618414  6.5579864  6.7783752  5.1849914  4.7945063
## 169  6.2115733  7.1066214  6.5784790  6.7157399  5.2726974  4.8363730
## 170  6.1179402  7.0293480  6.4865349  6.6423289  5.1725772  4.7247284
## 171  6.0685131  7.3956823  6.6443635  6.9406955  5.2975641  4.7535960
## 172  6.0319889  7.2687202  6.5364140  6.8043780  5.1870630  4.6469446
## 173  4.9058632  6.3117706  5.5438220  6.0308637  4.0053239  3.3120096
## 174  4.9595189  5.7435567  5.2275007  5.5740644  3.6965217  3.1819939
## 175  4.7509358  5.7987373  5.1243092  5.6027744  3.4320027  2.8861229
## 176  4.9675071  5.0023337  4.8056952  5.1187597  3.0603373  3.0511453
## 177  4.5162627  5.3468192  4.7413725  5.2781469  2.8863841  2.5199062
## 178  4.8103299  5.4322415  4.9065055  5.2939495  3.2718394  2.8586316
## 179  5.1342160  5.3120542  5.1055805  5.2981615  3.6239402  3.3596671
## 180  5.3654435  5.0187172  5.1692118  5.3167847  3.6375506  3.6040235
## 181  5.9594798  5.4064044  5.7647125  5.7289433  4.5640090  4.4844801
## 182  5.0378209  5.3755684  5.1958360  5.5093223  3.5212551  3.2646267
## 183  5.7136735  5.4765948  5.5836728  5.6414373  4.2849163  4.0952748
## 184  5.2924681  5.5852805  5.3621483  5.6036029  3.9115173  3.5405596
## 185  4.8140713  6.0675212  5.4151598  5.9465160  3.7912024  3.1286349
## 186  4.6539148  5.3993857  5.0097136  5.4730439  3.2630767  2.8249833
## 187  6.3960386  5.1816471  5.8919524  5.7303985  4.7581202  4.9693840
## 188  4.1448757  3.6133120  3.4706405  3.3482693  3.3563593  3.3783787
## 189  3.9878028  3.4333847  3.1234609  3.1564604  3.0073245  3.1413415
## 190  4.3986426  3.2771875  3.4393348  3.1709331  3.4696921  3.6498436
## 191  4.2945340  2.8055107  2.9779295  2.8421696  3.1312168  3.5597812
## 192  3.8673508  2.9213869  2.6138329  2.7099685  2.7453862  3.0407590
## 193  4.4600218  2.7825782  3.0493132  2.8289257  3.2599075  3.6894050
## 194  3.9749643  2.3031388  2.3755725  2.3407041  3.0823585  3.4821445
## 195  3.7659278  2.4219980  2.1747819  2.2505811  2.9122208  3.2307934
## 196  5.8856111  2.9127694  4.1348736  2.9795694  5.3091842  5.6896870
## 197  5.0196778  2.7127365  2.8580678  1.7747893  4.6245868  4.9041565
## 198  4.6867623  2.8666238  2.7182563  1.8513837  4.4853178  4.6788140
## 199  4.9524572  2.7421993  2.8933920  1.8137432  4.6447589  4.8909172
##             61         62         63         64         65         66
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62   1.1078029                                                       
## 63   1.4114758  1.7359429                                            
## 64   1.9044459  2.4932439  1.1459087                                 
## 65   2.9836576  3.2980285  2.1228333  1.7218952                      
## 66   3.7765719  4.3522871  3.5109380  3.3336373  3.9394693           
## 67   3.2777992  3.7981184  3.4573468  3.4421948  4.1837472  1.2421256
## 68   2.0611265  2.9603350  2.1164640  1.9399647  3.0196374  3.2917746
## 69   1.4843197  2.3187867  2.1981212  2.2757262  3.3846478  3.6722436
## 70   1.7063418  2.5537814  1.8276214  1.8242920  2.9068173  3.3548400
## 71   3.1102076  3.8276051  2.8069469  2.4486976  3.4298892  3.9674754
## 72   2.5549297  3.2901191  2.6487020  2.4878574  3.5770501  4.0346992
## 73   2.9900165  3.7625149  2.8233256  2.6122671  3.6375155  3.9615512
## 74   3.0092566  3.7546786  2.8348952  2.5108059  3.5385473  3.9778690
## 75   3.3911070  4.0614578  3.1848584  2.9594988  4.0194150  4.1099603
## 76   2.5512843  2.9209781  2.3937294  2.5663014  3.5869811  4.2114400
## 77   2.5028225  2.4297668  2.5038108  2.9773319  3.8262256  4.7071031
## 78   2.5503671  2.9051012  2.5549729  2.7660346  3.8109473  4.3068202
## 79   2.2587093  2.5492779  2.3054619  2.4988970  3.4917884  4.3365353
## 80   2.5264835  3.0549241  2.6376417  2.8046460  3.9093622  4.2039213
## 81   2.5837957  3.1485476  1.7873759  1.5664077  2.3337740  2.9744058
## 82   1.9276598  2.0380606  1.1064372  1.7178415  2.3406251  3.4267906
## 83   2.1143129  2.8120623  1.6882648  1.6163122  2.6331771  2.8751721
## 84   1.6748264  2.2766471  1.3697775  1.6543541  2.6564338  3.0255716
## 85   2.2420044  2.6422864  1.9736764  2.1163857  2.7512781  3.9904899
## 86   2.6314770  2.8898369  2.0157388  2.2624989  2.6549350  4.1047404
## 87   2.1204987  2.5826279  2.3221675  2.4741874  3.2394382  4.1244174
## 88   2.3570839  2.6278691  2.2382622  2.6569652  3.3158983  4.2000010
## 89   3.3184037  3.1167534  2.6312197  3.1669807  3.3148107  4.7414985
## 90   3.4271090  3.5050422  2.6777581  2.8985429  3.0418803  4.4392259
## 91   2.8087354  2.8644293  2.5513400  2.9867167  3.4750949  4.3964311
## 92   2.8268266  2.7893471  2.5514728  3.0859223  3.5295943  4.5027442
## 93   2.7496249  2.9800484  2.4431755  2.7268317  3.6865820  3.6266835
## 94   3.0471481  3.5706931  2.7923655  2.8464343  3.8825082  3.3891419
## 95   2.5690394  2.4894992  2.5046666  3.0569563  3.9252221  4.0707843
## 96   3.0447463  3.2218595  2.5125160  2.7671949  3.0324180  4.2271538
## 97   2.4534166  2.4888381  2.4693629  2.9506785  3.4662758  4.4075432
## 98   4.7841505  4.7299306  3.7670408  3.8028307  3.3457697  5.3386331
## 99   4.9577359  5.2267506  4.0223168  3.7525159  3.4270818  5.0178482
## 100  3.8247461  3.8966210  2.9716783  3.0379131  2.9270706  4.6181463
## 101  3.2197961  3.1125124  2.7894146  3.2210014  3.9004829  5.2587424
## 102  3.2169545  3.2020463  2.6986263  3.0838150  3.8300957  5.1007879
## 103  4.6045830  4.2981222  4.5504804  4.9411964  5.5752075  6.4352157
## 104  2.8268179  2.5680262  2.9621572  3.5621974  4.4559960  5.4550123
## 105  2.9726384  2.6982741  3.0294661  3.6582297  4.5112025  5.5057246
## 106  3.1372519  2.7954710  3.4875798  4.1073096  4.9527251  5.8478658
## 107  3.1043337  2.8048744  3.5456096  4.0900130  4.9669701  5.8477037
## 108  3.0331084  2.8044137  3.1775087  3.7342471  4.6228974  5.5361966
## 109  3.1645149  2.7726261  3.0734185  3.7054972  4.4758450  5.6295121
## 110  2.9737993  2.6377681  3.1415880  3.7047705  4.5611951  5.6137638
## 111  2.7700111  2.9449463  2.8482647  3.1289482  4.2074306  4.9877417
## 112  3.3417042  3.1669201  3.0304291  3.4874517  4.1499994  4.9933761
## 113  3.2254949  2.9322166  3.5429492  4.1157333  4.8921746  5.4508341
## 114  3.2360226  2.8851054  3.5101316  4.0601906  4.8053070  5.4812667
## 115  3.2505054  3.0455584  3.2154369  3.8005149  4.5933805  5.1133681
## 116  3.1845851  2.9070830  3.4950531  4.0401544  4.8442490  5.3666480
## 117  2.9994097  2.9627622  3.0360855  3.4910457  4.3293284  4.8654768
## 118  3.0149860  2.8788830  3.0735298  3.6805277  4.4918464  4.9997797
## 119  3.0983205  3.0212062  3.4098782  3.8432567  4.7089950  5.1163725
## 120  2.9012478  2.9837580  3.2419787  3.6778817  4.6289442  4.8926719
## 121  4.2389904  4.2486790  4.4283507  4.7581883  5.6187780  6.1214895
## 122  4.3045848  4.1640658  4.4547540  4.8719576  5.6779088  6.2961999
## 123  4.4346127  4.2094925  4.6877542  5.1076782  5.8758426  6.5660508
## 124  4.7697218  4.4696531  5.2439209  5.6071406  6.4001829  7.0531453
## 125  4.4602895  4.2099311  4.7414407  5.2012785  5.9861309  6.6281037
## 126  4.3889372  4.2224754  4.5447571  4.9773059  5.7504833  6.3981303
## 127  4.9218799  4.6362485  5.5032826  5.8657988  6.6955742  7.2347385
## 128  4.3586697  4.1047308  4.7153715  5.2289968  6.2490537  6.7935675
## 129  4.4529571  4.1285160  4.5069206  4.9746549  5.9047120  6.6996967
## 130  4.3390671  4.0857680  4.7620455  5.2641171  6.3143929  6.8263321
## 131  4.3694871  4.0673177  4.3239228  4.8189887  5.7220217  6.5668234
## 132  4.2815707  4.0078704  4.2666531  4.7727471  5.6879463  6.5111564
## 133  4.3137093  4.0649142  4.2169007  4.7104778  5.5626258  6.4689297
## 134  4.1322751  3.9001185  4.3836925  4.8972667  5.8834172  6.5644801
## 135  4.4780245  4.1484170  4.8198039  5.3105589  6.2818327  6.9049482
## 136  4.3598638  4.0404653  4.4900610  4.9394298  5.8801806  6.6933392
## 137  4.2894358  4.0326320  4.5561495  5.0289474  6.0335762  6.6721472
## 138  4.4426732  4.1155782  4.4755033  4.9542628  5.8949031  6.6739892
## 139  4.5550756  4.2287889  4.9780933  5.4410807  6.4689565  7.0339769
## 140  4.4662795  4.1576286  4.6942142  5.1469224  6.1096135  6.8207153
## 141  4.6785426  4.3501668  5.0676126  5.4306101  6.4451566  7.0852715
## 142  5.4745065  5.2085860  6.2950253  6.6471902  7.6280120  8.0591208
## 143  7.3291668  7.1290477  7.7739916  8.0899235  8.7551240  8.8034969
## 144  6.1271555  5.8962860  6.6174049  6.9705177  7.6952073  7.7991651
## 145  6.3869436  6.1874207  7.0514031  7.4194408  8.2136194  8.1504214
## 146  6.6621423  6.3172122  7.0217795  7.2924169  7.9482290  8.1824755
## 147  6.3161991  6.0462532  6.5813861  6.9906225  7.6503246  7.7262505
## 148  6.3257685  6.1478794  6.9797525  7.3234456  8.0942765  8.0708602
## 149  6.1815871  6.0019006  6.7537800  7.0693205  7.8002864  7.8608717
## 150  5.8950572  5.6819649  6.2793071  6.6524011  7.3873680  7.4527271
## 151  5.7754493  5.5776337  5.8427529  6.2313550  6.8343779  7.0816126
## 152  5.8100828  5.6363377  6.0474715  6.5218385  7.1838692  7.2405660
## 153  7.0235148  6.9510340  7.3069299  7.7139903  8.3873052  8.2164395
## 154  5.9388430  5.7136870  6.1555443  6.5640673  7.2054826  7.3470688
## 155  7.0020561  6.8073213  7.1025991  7.4280708  7.9940051  8.1581653
## 156  7.6913125  7.5051737  7.7945434  8.0411800  8.6045195  8.6732987
## 157  6.6822143  6.4519817  7.0172012  7.4153509  8.1030541  8.0449903
## 158  5.6102016  5.4980034  5.0841139  5.3999806  5.4769791  6.2401406
## 159  4.8099776  4.6120523  4.6812366  5.2379655  5.7241363  5.9482486
## 160  5.9116352  5.7104772  5.7235904  6.1395126  6.6419033  6.9868235
## 161  6.2580203  6.1485055  6.0816577  6.4597659  6.8197197  7.0354233
## 162  6.3758477  6.3342426  5.6591335  5.8275406  5.6969806  6.6467351
## 163  7.6690548  7.5866488  7.0209633  7.1593515  6.9998981  7.9137264
## 164  7.9416647  7.8442761  7.2290944  7.2837742  7.0842471  8.0982518
## 165  4.4279738  4.2921416  4.5232406  5.0065857  5.5923723  5.7797873
## 166  4.8587245  4.6578491  4.8120476  5.2511031  5.7310822  6.0136539
## 167  6.6031037  6.4956260  5.8461783  5.9714246  5.7786593  6.8912658
## 168  4.7364259  4.6319302  4.8349861  5.1959048  5.7800671  5.8953694
## 169  4.7531216  4.5084875  4.6792931  5.1239470  5.6152720  5.9607819
## 170  4.6429580  4.3971559  4.5595409  5.0020543  5.5174912  5.8716241
## 171  4.5653494  4.3067652  4.7756886  5.2511092  5.8939176  6.0422061
## 172  4.4886237  4.2560863  4.6172876  5.1404712  5.7505875  5.9253930
## 173  3.0633852  2.9317644  3.4349866  4.0169663  4.4997046  5.0789384
## 174  3.2033290  3.0538944  2.9640611  3.5168784  3.8786904  4.7261399
## 175  2.9432443  3.0330520  3.0161996  3.5218810  4.0826286  4.5193631
## 176  3.5522620  3.9617040  3.0919387  3.1133167  3.5606187  4.0519499
## 177  2.7681734  3.1144715  2.7904584  3.0311196  3.6793854  4.0944396
## 178  3.0168627  3.0528167  2.6807249  3.1998716  3.5732533  4.3876644
## 179  3.5562342  3.5375900  2.9783922  3.3205434  3.4663296  4.6049412
## 180  3.9579215  4.1340430  3.2444222  3.3614624  3.2815491  4.7159041
## 181  4.6756883  4.5693544  3.8430048  3.9605411  3.5714925  5.5001752
## 182  3.4425727  3.6671858  3.2112116  3.4671744  3.6143827  4.7186618
## 183  4.2453364  4.1217517  3.4826004  3.8453621  3.5447782  5.3057171
## 184  3.5933767  3.4401297  3.0628914  3.6329015  3.5564872  5.0705455
## 185  2.8793035  2.7707952  3.1871371  3.7760350  4.1008608  5.0997163
## 186  2.8388629  2.9447155  2.8193912  3.1389949  3.4185423  4.6295220
## 187  5.3436778  5.5164650  4.4457100  4.2750535  3.7545516  5.5772529
## 188  3.7786661  4.1012806  3.2599697  3.2278011  3.5418358  2.5670356
## 189  3.6483251  4.1166558  3.1647255  3.0749347  3.4979327  2.1031489
## 190  4.0931996  4.4142666  3.3732423  3.1967105  3.2893455  2.7122955
## 191  4.0732114  4.5991021  3.4241779  3.0030279  3.0255738  2.4065123
## 192  3.5340533  4.0323600  2.9376004  2.6901586  2.9157429  1.9732127
## 193  4.2199561  4.6860560  3.4274915  3.0563277  2.9935491  2.5319397
## 194  4.0513413  4.6423479  3.5348811  3.1230119  3.3157265  1.5562377
## 195  3.7685564  4.3295218  3.2901121  3.0118962  3.2487240  1.3235146
## 196  6.0997076  6.4075535  5.2917072  4.9452858  4.4716111  3.8714788
## 197  5.2531646  5.5705697  4.6633183  4.4134499  4.1660835  2.5188891
## 198  4.9396751  5.2185802  4.5243420  4.2745496  4.1350299  2.3917803
## 199  5.1854593  5.4756982  4.6469844  4.3860868  4.1059347  2.6228417
##             67         68         69         70         71         72
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68   3.2439969                                                       
## 69   3.2467449  1.0960258                                            
## 70   3.2109419  0.4400981  0.8349648                                 
## 71   4.1879048  1.4663337  2.2490475  1.6906944                      
## 72   3.9810355  1.1458513  1.5438053  1.2512095  0.9200283           
## 73   4.1061429  1.2718829  2.0385054  1.5151609  0.5571333  0.7424370
## 74   4.1264205  1.3451496  2.0708767  1.5786752  0.2935960  0.6827139
## 75   4.2887480  1.8103261  2.4532734  2.0002963  0.8945683  1.1840994
## 76   4.1498724  1.8476003  1.9847887  1.6936598  1.6506318  1.3531688
## 77   4.4541889  2.6594300  2.3874424  2.3552147  2.7318548  2.2958812
## 78   4.1666332  1.9376445  1.9377815  1.7713949  1.8175386  1.3870805
## 79   4.1384204  1.9687586  1.8204012  1.7262684  2.0280941  1.5660670
## 80   4.0569698  1.6372526  1.7046371  1.5355923  1.6375981  1.0928253
## 81   3.3247885  1.7271765  2.4276198  1.7408267  1.8124832  2.0946451
## 82   3.4164462  2.2266832  2.3422772  1.9415042  2.6811004  2.5675626
## 83   3.0047830  1.1828939  1.8008566  1.1725082  1.6806352  1.6766731
## 84   2.9660655  1.3247338  1.5873201  1.1135409  2.0345827  1.8048480
## 85   3.9512303  1.7380955  1.9197108  1.5586899  1.8950061  1.7003325
## 86   4.2063113  2.1835052  2.5087009  2.0215900  2.1461662  2.1595200
## 87   3.8975300  1.7338370  1.6020953  1.5447661  2.0827223  1.5940177
## 88   4.0718101  2.0627660  2.0773008  1.8443016  2.2792270  1.9495151
## 89   4.7973498  3.4085390  3.5040545  3.1609205  3.4159567  3.3984777
## 90   4.6492751  3.0540984  3.3894150  2.9164058  2.8448777  3.0034722
## 91   4.3031582  2.6768125  2.6788434  2.4560139  2.7904914  2.5800250
## 92   4.3877167  2.8428011  2.7980893  2.5924594  3.0038005  2.7745478
## 93   3.6032005  2.5398380  2.6712711  2.3890743  2.3936784  2.2566321
## 94   3.5077820  2.2271349  2.6361381  2.2481066  1.8999850  1.8956362
## 95   3.8024699  2.9867995  2.7814629  2.7135808  3.1202104  2.7669060
## 96   4.3352045  2.5551432  2.8566844  2.4181362  2.4914254  2.4988347
## 97   4.1606334  2.5168294  2.3002772  2.2374283  2.8603957  2.4699864
## 98   5.7696873  4.4839448  4.9277742  4.3792722  4.0938531  4.4652163
## 99   5.6041515  4.1218538  4.8042525  4.1670656  3.5237248  4.0726255
## 100  4.9267006  3.3916621  3.8037379  3.2852547  3.0776855  3.3534089
## 101  5.2300205  3.3984331  3.4341517  3.1801715  3.2391204  3.1261243
## 102  5.1381794  3.2070870  3.3405897  3.0201163  2.9650160  2.9270492
## 103  6.2564211  4.9177431  4.7636792  4.7313526  4.8537725  4.5705192
## 104  5.1311500  3.4299083  3.0592915  3.1310409  3.5894414  3.1440454
## 105  5.2132953  3.5368023  3.2159145  3.2438272  3.6596526  3.2496107
## 106  5.4066208  3.9001430  3.3977261  3.5929787  4.1380374  3.6021982
## 107  5.3741793  3.8650702  3.3185196  3.5663019  4.1090931  3.5457897
## 108  5.2191138  3.5468379  3.2004353  3.2705044  3.6433225  3.2078585
## 109  5.3784876  3.7859938  3.4961175  3.4819567  3.8521674  3.5173559
## 110  5.2625601  3.6538934  3.2407460  3.3499477  3.7971636  3.3501979
## 111  4.7962418  2.7255812  2.5924499  2.5509235  2.6593491  2.2985078
## 112  4.8922132  3.4624155  3.3906390  3.2188066  3.3877350  3.2125491
## 113  4.9988458  3.7884484  3.2983985  3.4855307  4.0460810  3.5262821
## 114  5.0398448  3.8534906  3.3617891  3.5412952  4.0908678  3.5984731
## 115  4.8620532  3.4919517  3.2476097  3.2224892  3.5741932  3.2239796
## 116  4.9311206  3.6809659  3.2122306  3.3897861  3.9078479  3.3818312
## 117  4.6167223  3.0988797  2.8815110  2.8574484  3.1836047  2.8111074
## 118  4.7085409  3.2774547  2.9989301  3.0011945  3.4659310  3.0520153
## 119  4.7301048  3.3311067  2.9484857  3.0898887  3.4978533  2.9790582
## 120  4.5155931  2.9857321  2.6215959  2.7588554  3.2156170  2.6788224
## 121  5.8440479  4.3979128  4.1749596  4.2370760  4.0283335  3.6411635
## 122  5.9974233  4.6424260  4.3671233  4.4382717  4.3242330  3.9337199
## 123  6.1868224  4.9376522  4.5622218  4.7091560  4.6987766  4.2533491
## 124  6.5279965  5.4473281  4.9006019  5.2026518  5.3126316  4.7750168
## 125  6.2243642  5.0018796  4.5965811  4.7641355  4.7993348  4.3312584
## 126  6.0885664  4.7680186  4.4808848  4.5571196  4.4680055  4.0738881
## 127  6.6484463  5.6176441  5.0140324  5.3767747  5.5348760  4.9455963
## 128  6.3569552  4.9588358  4.5021246  4.7125553  4.9209532  4.4167782
## 129  6.4126320  4.9837514  4.6695013  4.7378896  4.7742046  4.4394451
## 130  6.3522524  4.9742122  4.4692447  4.7241984  4.9720997  4.4382454
## 131  6.3353421  4.8530813  4.6068271  4.6114550  4.6260702  4.3332377
## 132  6.2683898  4.7626146  4.5117262  4.5224077  4.5632202  4.2492056
## 133  6.2777703  4.7418034  4.5605966  4.5132564  4.5046174  4.2342752
## 134  6.1902225  4.7067553  4.3205079  4.4611303  4.6481979  4.1886452
## 135  6.4731713  5.1156724  4.6648355  4.8700456  5.0695213  4.5587213
## 136  6.3661518  4.9401367  4.5812425  4.6898937  4.7731715  4.3983209
## 137  6.2886306  4.8457975  4.4422887  4.6051328  4.7379552  4.2840776
## 138  6.3973317  4.9611616  4.6562525  4.7151522  4.7453797  4.4191706
## 139  6.5430995  5.2443780  4.7076637  4.9865217  5.2117278  4.6918368
## 140  6.4441921  5.0583839  4.6522582  4.8106821  4.9211940  4.4998411
## 141  6.6169660  5.3327152  4.8125754  5.0859978  5.2255949  4.7490127
## 142  7.3323548  6.3108922  5.5682996  6.0688770  6.4747671  5.7986392
## 143  8.2860623  7.8514105  7.3917629  7.6690182  7.9706554  7.5379491
## 144  7.2399718  6.7241766  6.2127919  6.5152489  6.8463017  6.3607699
## 145  7.4797745  7.0264096  6.4201166  6.8198820  7.2455086  6.6726228
## 146  7.7082131  7.2222069  6.7735530  7.0236462  7.2024257  6.7857457
## 147  7.3311609  6.7551988  6.4152047  6.5702254  6.7667559  6.3651999
## 148  7.4157202  6.9433139  6.3580232  6.7437951  7.1500196  6.5861705
## 149  7.2674334  6.7519945  6.2263922  6.5596223  6.8967788  6.3746083
## 150  6.9738126  6.3916391  5.9619777  6.1945121  6.4581698  6.0172635
## 151  6.8137100  6.1259743  5.9017912  5.9428499  6.0600848  5.7823575
## 152  6.8661781  6.2143102  5.9118104  6.0271973  6.2793447  5.8889115
## 153  7.8529709  7.2911912  7.0191585  7.1521587  7.3863440  7.0218369
## 154  6.9858473  6.3511640  6.0479092  6.1661033  6.3523383  5.9793073
## 155  7.8887239  7.3252280  7.0951501  7.1659701  7.2799972  7.0200978
## 156  8.4430327  7.9002103  7.7164939  7.7780476  7.7825227  7.5371202
## 157  7.6235035  7.0779667  6.7293402  6.9123162  7.1265605  6.6936942
## 158  6.3940185  5.4878484  5.6901619  5.3530251  5.1236930  5.1780095
## 159  5.7793907  4.9206796  4.8121387  4.7127103  4.8218986  4.5683555
## 160  6.8871985  6.1473499  6.0783067  5.9766212  5.9865952  5.8410154
## 161  6.9717411  6.2388702  6.2325548  6.1015987  6.0884956  5.9567658
## 162  6.9946787  6.0850059  6.4557851  6.0037366  5.5857621  5.8169347
## 163  8.2292970  7.4773509  7.7841277  7.3955681  7.0548376  7.2651113
## 164  8.4665334  7.7252022  8.0569163  7.6508141  7.2294982  7.5019205
## 165  5.4749848  4.6087663  4.3654069  4.3922938  4.6136595  4.2501943
## 166  5.8154271  4.9693846  4.8353803  4.7788979  4.8462788  4.5603724
## 167  7.2471279  6.3844150  6.7320964  6.2892147  5.8572082  6.1117598
## 168  5.6384627  4.7631429  4.5902365  4.5990186  4.6564431  4.3105564
## 169  5.7557143  4.9174877  4.7546852  4.7067458  4.7766283  4.5063658
## 170  5.6638451  4.8170883  4.6420035  4.5988480  4.6798713  4.4167766
## 171  5.6483194  4.8757714  4.5167739  4.6419531  4.8988550  4.4625348
## 172  5.5779871  4.7695721  4.4632660  4.5323303  4.7950048  4.3965059
## 173  4.6123966  3.5400152  3.0987568  3.2587436  3.9944882  3.4578363
## 174  4.5787924  3.3617517  3.2671891  3.1080857  3.5227397  3.2891083
## 175  4.2670257  2.9130989  2.7552228  2.6962594  3.2161345  2.8301250
## 176  4.2891712  2.6062656  3.1073281  2.6254655  2.3369205  2.5116408
## 177  3.9436850  2.3003839  2.3218859  2.1687085  2.5405636  2.2331029
## 178  4.3280050  2.9300221  2.9841104  2.7130226  3.1113009  2.9320126
## 179  4.7051784  3.3943202  3.5893353  3.2208118  3.3150616  3.3337038
## 180  5.0072956  3.5003471  3.9414906  3.4365019  3.1998175  3.4202874
## 181  5.7922783  4.5931570  4.9096964  4.4612234  4.2718367  4.5069309
## 182  4.7124872  3.1949919  3.3777887  3.0874199  3.2134629  3.0872696
## 183  5.5065169  4.2656352  4.5261067  4.0966694  4.1153103  4.2252483
## 184  5.0842555  3.7996267  3.8932958  3.5745292  3.8746270  3.7843379
## 185  4.6885267  3.4437191  3.0683938  3.1644998  3.8907627  3.3816614
## 186  4.4410494  2.9378902  2.8541493  2.7371038  3.1405511  2.8352018
## 187  6.0995126  4.8097879  5.3936119  4.8121901  4.3098133  4.7498420
## 188  2.9559857  3.1942643  3.6117628  3.1770156  3.4148876  3.5658906
## 189  2.6006847  2.8308745  3.3524810  2.8746491  3.1478167  3.3151392
## 190  3.3110043  3.4611517  3.9921969  3.4687873  3.5621383  3.8580041
## 191  3.1259747  3.2233688  3.8786116  3.3203552  3.4383962  3.7673751
## 192  2.5669462  2.8072474  3.3615566  2.8441322  3.2365751  3.4474170
## 193  3.3349007  3.4096379  4.0893522  3.4865357  3.5623868  3.9509780
## 194  2.4346157  3.1781892  3.7948804  3.3053654  3.4677957  3.7579200
## 195  2.1229920  3.0060658  3.5605693  3.0942368  3.4264502  3.6283818
## 196  4.7143147  5.6419312  6.2424427  5.7031185  5.6885843  6.0998501
## 197  3.2328124  4.8526244  5.2813268  4.8715959  5.2458216  5.4865622
## 198  2.8453003  4.6773675  4.9711298  4.6691090  5.1583502  5.2898796
## 199  3.2232338  4.8709584  5.2476233  4.8738046  5.2856390  5.4896747
##             73         74         75         76         77         78
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74   0.4194399                                                       
## 75   0.9419931  0.8940489                                            
## 76   1.6566579  1.6226845  1.4588431                                 
## 77   2.7379503  2.6939649  2.5907701  1.1654828                      
## 78   1.7745584  1.7500887  1.5543552  0.3505725  1.0791085           
## 79   2.0439362  1.9709934  1.9288487  0.6235593  0.8935161  0.6117702
## 80   1.4451925  1.5129283  1.3397234  0.6837027  1.5535858  0.5728722
## 81   1.9979717  1.9373186  2.2171271  2.1362276  2.7670760  2.3257587
## 82   2.7543812  2.7343691  2.9666328  2.0959866  2.0899114  2.2232301
## 83   1.7001679  1.6996105  2.0479874  1.9149403  2.5630302  2.0356656
## 84   1.9885166  2.0132164  2.3372858  1.8192291  2.2264447  1.9012739
## 85   1.9595880  1.9030071  2.1972954  1.5837130  1.9327738  1.6507927
## 86   2.2640636  2.2261437  2.4212219  1.7866803  2.0493871  1.9171532
## 87   2.0420139  1.9931043  2.2757795  1.6845987  1.9405307  1.6080929
## 88   2.2195001  2.2473047  2.4104591  1.6557695  1.7822722  1.6215631
## 89   3.5325848  3.5064599  3.5178340  2.5953859  2.3093291  2.6831848
## 90   3.0424254  2.9724236  2.9693554  2.4010554  2.4966470  2.5257250
## 91   2.8191954  2.8016167  2.8225996  2.0068222  1.8993389  1.9846284
## 92   3.0153226  3.0157904  3.0338258  2.1247127  1.8892206  2.1035713
## 93   2.4369436  2.4140750  2.3004000  1.6119815  1.8221736  1.6407852
## 94   1.8814369  1.9043771  1.7337601  1.7490499  2.4326790  1.7878574
## 95   3.1036544  3.0991184  3.0300404  1.9553252  1.5504894  1.8932612
## 96   2.6151924  2.5556009  2.6458254  2.0684323  2.2213670  2.1517638
## 97   2.8372542  2.8223761  2.9334146  1.9991108  1.7462643  1.9174928
## 98   4.4220829  4.2944944  4.2835015  3.8382509  3.8463324  4.0174326
## 99   3.8884025  3.7414649  3.7179986  3.7999727  4.2004062  3.9859509
## 100  3.3597827  3.2432980  3.2621814  2.8053729  2.9157470  2.9559113
## 101  3.3525592  3.2955875  3.1643434  2.2366236  1.8962039  2.2464068
## 102  3.0863012  3.0377651  2.8925927  2.0683589  1.9250370  2.1123881
## 103  4.9144171  4.7949798  4.8700393  4.0755272  3.6863504  4.0670733
## 104  3.5617422  3.5446445  3.4662495  2.3322391  1.6415234  2.1866864
## 105  3.6341705  3.6256362  3.5238244  2.3995157  1.7072884  2.2646548
## 106  4.0791183  4.0644524  3.9764141  2.8565135  2.0582633  2.6544582
## 107  4.0612708  4.0246459  3.9492130  2.8678563  2.1030878  2.6486926
## 108  3.6258533  3.5964549  3.4839574  2.4171819  1.7563721  2.2497127
## 109  3.8797522  3.8487361  3.7485288  2.5823346  1.8196474  2.4910817
## 110  3.8010851  3.7544099  3.6787797  2.5331185  1.7613254  2.3808470
## 111  2.6677998  2.6111214  2.4951129  1.7538976  1.7124843  1.6090185
## 112  3.4756381  3.4245938  3.1158389  2.0450244  1.5447730  2.0225672
## 113  3.9936939  3.9753140  3.7387594  2.5785419  1.7522100  2.3724136
## 114  4.0738737  4.0332859  3.8123958  2.6176027  1.7401832  2.4329544
## 115  3.5490832  3.5504614  3.2484485  2.1269218  1.4977498  2.0015690
## 116  3.8644794  3.8256290  3.6146873  2.4600381  1.6636805  2.2652126
## 117  3.1681275  3.1475768  2.8392501  1.7847707  1.3345278  1.6385035
## 118  3.3930161  3.4215120  3.1412983  2.0067104  1.4187496  1.8651071
## 119  3.4533701  3.4040227  3.1628456  2.1509734  1.6030846  1.9395564
## 120  3.1053984  3.1153387  2.8294484  1.8998015  1.5773589  1.6607937
## 121  3.9805237  3.9644880  3.7781097  3.0960465  2.8328395  2.9521436
## 122  4.2921278  4.2719526  4.1042032  3.2566619  2.8096044  3.1250348
## 123  4.6788936  4.6362364  4.4890253  3.5728277  2.9911274  3.4165629
## 124  5.3042391  5.2208920  5.1157614  4.1884397  3.5177919  3.9906596
## 125  4.7588307  4.7304021  4.5846156  3.6448813  3.0365355  3.4808921
## 126  4.4381196  4.4181658  4.2415390  3.3760755  2.8831890  3.2375020
## 127  5.5005935  5.4212522  5.3265356  4.4301162  3.7707995  4.2099027
## 128  4.8411172  4.8386360  4.5700405  3.6151379  2.9882505  3.4237157
## 129  4.7983560  4.7545781  4.4614180  3.4715654  2.8309036  3.3548309
## 130  4.8835857  4.8796387  4.6288486  3.6761203  3.0528269  3.4757000
## 131  4.6455931  4.6197272  4.3226168  3.3308175  2.7347907  3.2456650
## 132  4.5621640  4.5486370  4.2540403  3.2669833  2.6892890  3.1761298
## 133  4.5194110  4.5029034  4.2023125  3.2388111  2.6961834  3.1716471
## 134  4.5813983  4.5822634  4.3229058  3.3407103  2.7439414  3.1881216
## 135  5.0212806  4.9722013  4.7975901  3.8061010  3.1546704  3.6574370
## 136  4.7916902  4.7408719  4.4698303  3.4676029  2.8108062  3.3389853
## 137  4.6990917  4.6718140  4.4026561  3.4412730  2.8239374  3.2749143
## 138  4.7666806  4.7277291  4.4347967  3.4425676  2.8125311  3.3327515
## 139  5.1680218  5.1271303  4.8844947  3.9109325  3.2226361  3.7096902
## 140  4.9183959  4.8715466  4.5923670  3.6171871  2.9503675  3.4545203
## 141  5.2424066  5.1540277  4.9152940  3.9790381  3.3074619  3.7882379
## 142  6.3962837  6.3300346  6.1631690  5.3187403  4.6547185  5.0539345
## 143  7.9169639  7.8845377  7.6094068  6.9841922  6.5583437  6.8278490
## 144  6.7945153  6.7530702  6.4288390  5.6891295  5.1710269  5.5058364
## 145  7.1415220  7.1185123  6.8246404  6.1139662  5.6055055  5.8976880
## 146  7.2459650  7.1163402  6.8786758  6.1202391  5.5779257  5.9917339
## 147  6.7263137  6.6778811  6.4049305  5.6770628  5.2217645  5.5681363
## 148  7.0554123  7.0250107  6.7294063  6.0354218  5.5407678  5.8223207
## 149  6.8342484  6.7836352  6.4816869  5.7903919  5.3042671  5.5956889
## 150  6.4061042  6.3729031  6.0347886  5.3122253  4.8456566  5.1548019
## 151  6.0511369  6.0321371  5.6359181  4.9357460  4.5388142  4.8464029
## 152  6.1840116  6.2077703  5.8415043  5.1338996  4.7257096  5.0091536
## 153  7.2558562  7.3033372  7.0000621  6.5010057  6.2549269  6.3868237
## 154  6.3128600  6.2815352  5.9534264  5.2302908  4.7927225  5.1203135
## 155  7.2727017  7.2432898  6.9445480  6.3575665  6.0326240  6.2853100
## 156  7.8028897  7.7227487  7.5106905  7.0132201  6.7518060  6.9646274
## 157  7.0558362  7.0128582  6.7911580  6.1292335  5.7340413  6.0206629
## 158  5.2477019  5.2108872  4.7892121  4.1827844  3.9455740  4.2356317
## 159  4.7768835  4.8111572  4.3991356  3.5280869  3.0778393  3.4666138
## 160  6.0028758  6.0009678  5.5875392  4.9168352  4.5926064  4.8924360
## 161  6.0822612  6.0946425  5.7736952  5.2300920  5.0109548  5.2110930
## 162  5.7809957  5.7226583  5.3136756  4.9227098  4.8460253  5.0293592
## 163  7.2385497  7.1806060  6.8549578  6.5009112  6.4028896  6.5941625
## 164  7.4692423  7.3759752  7.0618367  6.7378481  6.6577656  6.8496588
## 165  4.5494413  4.5706497  4.1755838  3.2932237  2.8342604  3.1778755
## 166  4.8480399  4.8084511  4.4881178  3.6475323  3.2123750  3.5976236
## 167  6.1023496  6.0078288  5.6258762  5.1868722  5.0531352  5.3037975
## 168  4.6382712  4.5861850  4.2754345  3.5335618  3.1946593  3.4523542
## 169  4.8018435  4.7574399  4.4000287  3.4928137  2.9816982  3.4338522
## 170  4.7082614  4.6681010  4.2983424  3.3703159  2.8551763  3.3120272
## 171  4.8543710  4.8241466  4.5192332  3.5627847  2.9884964  3.4388340
## 172  4.7333047  4.7398236  4.3893499  3.4267356  2.8707580  3.3113170
## 173  3.8896323  3.9088964  3.8450705  2.8787970  2.3245523  2.6940283
## 174  3.5430173  3.5363824  3.4301192  2.4815872  2.0786715  2.4390726
## 175  3.1206058  3.1613898  3.0626084  2.2781818  2.0941110  2.1562543
## 176  2.4432656  2.4121667  2.2533339  2.2584225  2.7902453  2.3326702
## 177  2.4871312  2.4883898  2.4394082  1.9419384  2.1700459  1.8739366
## 178  3.1008638  3.1309645  3.0468404  2.2260964  2.0996362  2.2339360
## 179  3.4513064  3.4009257  3.2782471  2.5710721  2.4522016  2.6338493
## 180  3.3946679  3.3302237  3.3476115  3.0478845  3.2167870  3.1464555
## 181  4.5590054  4.4315116  4.4356093  3.9017852  3.7703934  4.0173159
## 182  3.2530049  3.2308548  3.2697629  2.8342797  2.8601539  2.8025685
## 183  4.2878319  4.2378356  4.2433934  3.5809274  3.3743403  3.6700022
## 184  3.9325399  3.9372159  3.9735718  3.1426155  2.8150277  3.1730333
## 185  3.7998720  3.8159286  3.9235235  2.9961978  2.5014094  2.8505733
## 186  3.1755522  3.1191111  3.2502042  2.5329772  2.3515928  2.4653764
## 187  4.6358208  4.5020633  4.4997145  4.4239629  4.6443877  4.5804014
## 188  3.5534083  3.4930853  3.3280710  3.2069467  3.5279110  3.2916075
## 189  3.2302418  3.2075546  3.0929403  3.1445150  3.6398620  3.2500142
## 190  3.7769707  3.6889987  3.5637749  3.5098536  3.8820475  3.6554631
## 191  3.6341758  3.5469142  3.5528070  3.7221281  4.2828665  3.9002611
## 192  3.3577384  3.3172802  3.3345139  3.3316636  3.8407521  3.4974287
## 193  3.7732687  3.7002974  3.6877633  3.8122794  4.3526734  4.0139994
## 194  3.6061684  3.5471473  3.7116784  3.9825877  4.5831624  4.1243712
## 195  3.5135264  3.4823083  3.6649974  3.8120185  4.3566448  3.9455629
## 196  5.9440811  5.8406476  5.8667858  5.9765937  6.3249745  6.1423906
## 197  5.3982132  5.3401073  5.3964865  5.3764342  5.7164156  5.5294460
## 198  5.3060010  5.2167310  5.3110624  5.2019220  5.4685153  5.3269571
## 199  5.4497205  5.3727810  5.4359815  5.3643026  5.6537064  5.5062199
##             79         80         81         82         83         84
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80   0.9561883                                                       
## 81   2.3667646  2.3823590                                            
## 82   2.0788328  2.4479782  1.4191629                                 
## 83   2.1059084  1.9874649  0.7274435  1.4352243                      
## 84   1.9026113  1.9077781  1.1242704  1.0673286  0.6015669           
## 85   1.6433094  1.7971588  1.5648576  1.4963861  1.3749576  1.2615134
## 86   1.9407594  2.1428107  1.4923951  1.3648759  1.5773688  1.4948166
## 87   1.6295222  1.6792328  2.0470633  1.9251185  1.6404545  1.4590888
## 88   1.7523505  1.7807429  1.9840809  1.6474411  1.6980276  1.4398314
## 89   2.6615237  3.0527515  2.5775523  1.8493495  2.7356203  2.4969852
## 90   2.5763754  2.8479088  2.0271097  1.8859598  2.3176535  2.2875705
## 91   2.0791825  2.2727233  2.2763190  1.7978579  2.1628747  1.9213018
## 92   2.1710960  2.4045150  2.4327832  1.7960472  2.3256353  2.0307427
## 93   1.7685341  1.8751758  2.0710915  1.8958944  1.9613770  1.8355950
## 94   2.0854768  1.7693195  1.9582234  2.3855184  1.7837286  1.9074876
## 95   1.8615191  2.2001290  2.6959594  1.9685047  2.5021853  2.1528114
## 96   2.2473188  2.4201787  1.8249790  1.7206433  1.9281691  1.8506379
## 97   1.9297723  2.1768421  2.4226483  1.7818015  2.1695837  1.8222592
## 98   3.9705041  4.3898189  3.1061916  3.0676067  3.6739448  3.7316649
## 99   4.0482910  4.2285370  2.7909605  3.4096750  3.3917019  3.6701274
## 100  2.9608039  3.2979983  2.1685987  2.1801899  2.6184804  2.6669109
## 101  2.2528776  2.6582229  2.8038733  2.2786616  2.8764020  2.6751900
## 102  2.1821210  2.4963977  2.5811423  2.2030189  2.6761010  2.5296813
## 103  4.0680835  4.3601675  4.7806393  4.2987024  4.6892303  4.4238532
## 104  2.1583680  2.5376466  3.3840917  2.5935817  3.1665330  2.7963074
## 105  2.2687430  2.6261030  3.4107557  2.6153097  3.2235180  2.8587369
## 106  2.6171472  2.9777928  3.9501078  3.1107107  3.6825911  3.2820049
## 107  2.5882958  2.9642289  3.9776657  3.1890785  3.6899259  3.3057052
## 108  2.2734023  2.6124935  3.4630858  2.7428928  3.2542502  2.9114754
## 109  2.4435842  2.9077266  3.4966638  2.6234555  3.3936744  3.0329184
## 110  2.3094027  2.7659502  3.5694838  2.7479291  3.3728591  3.0023446
## 111  1.7575072  1.8819568  2.7508832  2.4913072  2.5179448  2.3434877
## 112  2.0289646  2.4763579  3.0566860  2.4492757  3.0566501  2.8150406
## 113  2.3258274  2.7129370  3.8980330  3.0985457  3.6343757  3.2511096
## 114  2.3307945  2.8108142  3.8996007  3.0631618  3.6715674  3.2892262
## 115  2.0841789  2.3805719  3.3896488  2.6945462  3.2191112  2.8955625
## 116  2.2336788  2.6138501  3.8167690  3.0640996  3.5467687  3.1681433
## 117  1.7126809  1.9991686  3.0903896  2.5533810  2.8923842  2.6176187
## 118  1.9330618  2.1791668  3.3187590  2.6292717  3.0890238  2.7458262
## 119  1.9866830  2.2516371  3.5264047  2.9781885  3.2376167  2.9255328
## 120  1.7878475  1.8625925  3.3275932  2.8677098  2.9776323  2.6906185
## 121  3.0220992  3.1377693  4.4609791  4.1105247  4.2555260  4.0605635
## 122  3.1455467  3.3744147  4.6273455  4.1188704  4.4470720  4.1965294
## 123  3.3747822  3.6934650  4.9436812  4.3470429  4.7506644  4.4669726
## 124  3.8833446  4.2690852  5.5837260  4.9323623  5.3364659  5.0267500
## 125  3.4472956  3.7470489  5.0432471  4.4099025  4.8293377  4.5269150
## 126  3.2500807  3.4989230  4.7250249  4.1878685  4.5525877  4.2938294
## 127  4.1156303  4.4557249  5.8550193  5.2112384  5.5617756  5.2436902
## 128  3.4210112  3.6624995  5.1561051  4.5032926  4.8968515  4.5776600
## 129  3.3204224  3.7055384  4.8751133  4.2231819  4.7620887  4.4831113
## 130  3.4575597  3.6967980  5.2403317  4.5806162  4.9543867  4.6287084
## 131  3.2218067  3.5882070  4.6967520  4.0567798  4.6113258  4.3397915
## 132  3.1571932  3.4950489  4.6542011  4.0222609  4.5480389  4.2728412
## 133  3.1548666  3.4989714  4.5520290  3.9562631  4.4883193  4.2316278
## 134  3.1590647  3.4335034  4.8488490  4.2063773  4.6273990  4.3176120
## 135  3.6101842  3.9205716  5.3167808  4.6540428  5.0722701  4.7356045
## 136  3.2732461  3.6783482  4.8978904  4.2381480  4.7594507  4.4715913
## 137  3.2556991  3.5532192  4.9583819  4.3307763  4.7441412  4.4443731
## 138  3.3067378  3.6811318  4.8511481  4.1978492  4.7391413  4.4595512
## 139  3.6579063  3.9823770  5.4474693  4.7583850  5.1872153  4.8614655
## 140  3.4116088  3.7752422  5.0796057  4.4249807  4.9031432  4.6083961
## 141  3.7052308  4.1037603  5.4631240  4.8199429  5.2442738  4.9505850
## 142  4.9458408  5.2368208  6.7822621  6.1277425  6.4143322  6.0825392
## 143  6.7876073  6.9697427  8.0699061  7.5709289  7.8281131  7.5850702
## 144  5.4513145  5.6862138  6.9396343  6.3738545  6.6794759  6.4043838
## 145  5.8539795  6.0200056  7.4261100  6.8546924  7.0834534  6.7888055
## 146  5.9099203  6.2580121  7.2989477  6.7590482  7.1174111  6.8527514
## 147  5.5735467  5.7640655  6.8584482  6.3439860  6.6572048  6.3849306
## 148  5.7727119  5.9470361  7.3251677  6.7790238  6.9940930  6.7104312
## 149  5.5418506  5.7498652  7.0465675  6.5294063  6.7575717  6.4898504
## 150  5.1360434  5.3346058  6.5614743  6.0328357  6.3228659  6.0591972
## 151  4.8531983  5.0662609  6.0178663  5.5423130  5.9098094  5.6915363
## 152  5.0460399  5.1548893  6.3137259  5.8024486  6.1032032  5.8411041
## 153  6.4556038  6.4389799  7.5241409  7.1439229  7.2817578  7.0684854
## 154  5.1263566  5.3172966  6.3963770  5.8956218  6.2180378  5.9622758
## 155  6.2842820  6.4609661  7.2928771  6.8763010  7.1768559  6.9796029
## 156  6.9817742  7.1377297  7.9054264  7.5928915  7.7918254  7.6166531
## 157  6.0434989  6.1666862  7.3028537  6.8347817  7.0582274  6.7878417
## 158  4.2630572  4.5581726  4.7877893  4.5179459  5.0079332  4.9155432
## 159  3.5476373  3.7276885  4.7448233  4.1935861  4.6667869  4.4104659
## 160  4.9262732  5.1284049  5.8429200  5.4074353  5.8344022  5.6477765
## 161  5.2757524  5.3920751  6.0294406  5.7030075  6.0140395  5.8601257
## 162  5.0565034  5.3381797  5.1626075  5.1047284  5.5268542  5.5376394
## 163  6.5916897  6.8670560  6.6548142  6.5673597  6.9808843  6.9835059
## 164  6.8258910  7.1521423  6.8139104  6.7688958  7.1951019  7.2271528
## 165  3.1986356  3.4007254  4.6523491  4.1050164  4.4838409  4.2179319
## 166  3.6226483  3.8743222  4.8622614  4.3770879  4.7757746  4.5290841
## 167  5.2859200  5.6585548  5.3817263  5.2827591  5.7897728  5.7978515
## 168  3.4954699  3.6766729  4.8296363  4.4422520  4.6732485  4.4476296
## 169  3.4378943  3.7577203  4.7429857  4.1980126  4.6781038  4.4256780
## 170  3.3041627  3.6410724  4.6446378  4.0826657  4.5799066  4.3279494
## 171  3.4207629  3.6970725  5.0096787  4.3927064  4.8005304  4.4901220
## 172  3.3147909  3.5595953  4.8414941  4.2134480  4.6550089  4.3501461
## 173  2.6899163  2.9071523  3.6399373  2.9066439  3.3274908  2.9412512
## 174  2.4764743  2.7731832  2.9294496  2.2440873  2.8632472  2.5680741
## 175  2.2989656  2.3331035  2.8962896  2.4270021  2.6241412  2.3398741
## 176  2.5762286  2.4405945  2.0476816  2.5091758  2.1243595  2.2838767
## 177  2.0290293  1.9621190  2.3845035  2.2985298  2.0998039  1.9711438
## 178  2.3150573  2.4769482  2.5351051  2.0343423  2.4625484  2.2198242
## 179  2.6737280  2.9779665  2.5646135  2.2133993  2.7426203  2.6189673
## 180  3.2413655  3.4048280  2.3571846  2.5045259  2.7042423  2.7741355
## 181  3.9703029  4.4069635  3.2872472  3.0995976  3.7485071  3.7401770
## 182  2.9058897  2.9946443  2.6047576  2.5200448  2.6060363  2.5291222
## 183  3.6606497  4.0203474  3.1110570  2.7216018  3.4514942  3.3449136
## 184  3.1738110  3.4850751  2.9640209  2.3130988  3.0910523  2.8490282
## 185  2.8156968  3.0546147  3.3961640  2.6454005  3.1154201  2.7232173
## 186  2.4514490  2.7094182  2.5804288  2.1658313  2.4485807  2.2221837
## 187  4.5974903  4.8521251  3.4583995  3.8445401  4.0209693  4.2165274
## 188  3.3727729  3.4284497  2.2927118  2.6207594  2.4758905  2.5978544
## 189  3.3607069  3.2735512  2.1624804  2.6927309  2.2525040  2.4409962
## 190  3.6811071  3.8064471  2.3547549  2.8138334  2.7197078  2.9139928
## 191  3.8779463  3.9217748  2.4314343  3.1658455  2.7347710  3.0260245
## 192  3.4710760  3.5022654  2.1731295  2.6979289  2.3422802  2.5390096
## 193  3.9933364  4.0619167  2.4611491  3.1519435  2.8479156  3.1302283
## 194  4.1588932  4.0850653  2.4399381  3.2429129  2.6038155  2.9258091
## 195  3.9772407  3.9016885  2.3464922  3.0007914  2.4309349  2.6762408
## 196  6.1155637  6.2698611  4.3619839  4.8980049  4.8293325  5.0789993
## 197  5.4589030  5.5777310  4.0651100  4.3970061  4.2999230  4.4479269
## 198  5.2223986  5.3890876  4.0409873  4.2637795  4.1846183  4.2751254
## 199  5.4078890  5.5749865  4.0885338  4.3657882  4.3159740  4.4423150
##             85         86         87         88         89         90
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86   0.7090467                                                       
## 87   0.7423311  1.3802145                                            
## 88   0.7383552  0.9665519  0.8270095                                 
## 89   1.9117779  1.4428416  2.3917779  1.7848578                      
## 90   1.5894711  1.0266290  2.1618222  1.6915342  0.9990823           
## 91   1.1716622  1.0944104  1.3746312  0.8181816  1.2140468  1.2465453
## 92   1.3612719  1.2231547  1.5705774  0.9547487  1.0617089  1.3209338
## 93   2.0622710  2.0742872  2.2136914  2.0259588  2.5696722  2.4321291
## 94   2.2182443  2.3090970  2.3140572  2.2504925  3.1522777  2.7626410
## 95   2.3345556  2.3747213  2.3634885  2.1360790  2.5174634  2.7115154
## 96   1.1627001  0.7319296  1.6266822  1.1683205  1.4006269  0.8983158
## 97   1.1623194  1.3406265  1.1005825  0.7418024  1.6386009  1.7804856
## 98   3.2239448  2.6240070  3.8299728  3.4478848  2.3038467  1.8927353
## 99   3.1981298  2.7120646  3.7535089  3.5347212  3.0786428  2.2192535
## 100  2.0441919  1.4747777  2.6328119  2.2658930  1.5210346  0.7974308
## 101  2.2899306  2.0492374  2.5232133  2.1564573  2.0118451  2.0613180
## 102  2.1576073  1.8970256  2.4492558  2.0559842  1.9782036  1.9313643
## 103  4.3021383  4.2442204  4.3190804  4.1201882  4.2048009  4.3927319
## 104  2.5012884  2.5759186  2.3974683  2.1639561  2.5229081  2.8521724
## 105  2.5626762  2.5750657  2.4987385  2.1935776  2.4486594  2.7964580
## 106  3.0017048  3.1206649  2.7679095  2.6047380  3.0090967  3.3767678
## 107  3.0068418  3.1883267  2.7153136  2.6563728  3.1630259  3.4726663
## 108  2.5873619  2.6529019  2.4521093  2.2258818  2.6059358  2.8798904
## 109  2.7029032  2.6345716  2.7384929  2.3911413  2.2966848  2.7317440
## 110  2.6713875  2.7508736  2.5499941  2.3663055  2.6239314  2.9699697
## 111  1.9960025  2.1870365  1.8619694  1.8197205  2.6687529  2.5800637
## 112  2.3339989  2.1806638  2.5098349  2.1452998  1.7521902  1.9838147
## 113  2.8776870  3.0130921  2.6547171  2.5064254  2.7513611  3.1248530
## 114  2.8883025  3.0098520  2.7045244  2.5710371  2.6836534  3.0817349
## 115  2.5066765  2.4950581  2.4916086  2.1264182  2.1371544  2.4965989
## 116  2.8116514  2.9535608  2.5898413  2.4528033  2.7571746  3.0937393
## 117  2.1886243  2.2684097  2.1153015  1.8994591  2.2285764  2.3736341
## 118  2.4038044  2.4493937  2.3365981  2.0127451  2.2542558  2.5770216
## 119  2.5540192  2.7419919  2.2911826  2.2313506  2.7893226  2.9377245
## 120  2.3510872  2.6040364  2.0557668  2.0083674  2.7896195  2.8928212
## 121  3.7536671  3.8672413  3.5978818  3.5434821  4.0730022  4.1309929
## 122  3.8850671  3.9507573  3.7684574  3.6441438  3.9749641  4.1573470
## 123  4.1360991  4.2306418  3.9671372  3.8958128  4.1947573  4.4219849
## 124  4.6830612  4.8806749  4.3990998  4.4658656  4.8357982  5.0930153
## 125  4.2137034  4.3153438  4.0322227  3.9433982  4.2486403  4.5177858
## 126  3.9727637  4.0248034  3.8511669  3.7189912  4.0110625  4.2062833
## 127  4.9225004  5.1645036  4.5774873  4.6840777  5.1576676  5.4147867
## 128  4.3917973  4.5201146  4.1764437  4.0814000  4.4342900  4.7335816
## 129  4.2266089  4.2315397  4.1774299  3.9969407  3.9821576  4.2834867
## 130  4.4506729  4.6182966  4.2061095  4.1489982  4.5540088  4.8625932
## 131  4.1068438  4.0632311  4.1154543  3.8814059  3.8114745  4.1102066
## 132  4.0583836  4.0281800  4.0513623  3.8242091  3.8235187  4.1121008
## 133  4.0155554  3.9335399  4.0500450  3.7986975  3.7434672  3.9873232
## 134  4.1452969  4.2323049  3.9980223  3.8744065  4.1686377  4.4499245
## 135  4.5878083  4.6984971  4.3980155  4.3151330  4.6246438  4.9295325
## 136  4.2194680  4.2636783  4.1341800  4.0048360  4.0660305  4.3580176
## 137  4.2351023  4.3345251  4.0683888  3.9678701  4.2426898  4.5144897
## 138  4.2114511  4.2103306  4.1751783  3.9779958  3.9494237  4.2629628
## 139  4.6373917  4.8073873  4.3914644  4.3615792  4.6723261  4.9972385
## 140  4.3552632  4.4344582  4.2076828  4.1064100  4.2610167  4.5470324
## 141  4.6742172  4.8502362  4.4414996  4.4658851  4.7173829  4.9925903
## 142  5.8681572  6.1893580  5.4125710  5.6167612  6.2182753  6.4748437
## 143  7.2745883  7.4527275  7.0195955  7.0712136  7.1726036  7.4007289
## 144  6.0291013  6.2237407  5.7394765  5.7978031  5.8923691  6.1452270
## 145  6.4630949  6.7330225  6.0819435  6.1985184  6.4934942  6.7587438
## 146  6.4781410  6.6137127  6.2672365  6.3127929  6.2364883  6.4734402
## 147  6.0940925  6.1601837  5.9313087  5.8376602  5.7959582  6.0515426
## 148  6.3760416  6.6406906  5.9975951  6.1278659  6.4282408  6.6608942
## 149  6.1327394  6.3609520  5.7940319  5.9094764  6.1384774  6.3368659
## 150  5.6977782  5.8486255  5.4632923  5.4570407  5.5018326  5.7473422
## 151  5.3031296  5.2972309  5.2415917  5.0903742  4.8264409  5.0368850
## 152  5.5350979  5.5860583  5.3805741  5.2389770  5.2137484  5.4640234
## 153  6.8611032  6.9576053  6.6868987  6.5960814  6.7494918  6.9402906
## 154  5.6323536  5.6795077  5.4908887  5.3839075  5.2984960  5.5279449
## 155  6.6767596  6.7015199  6.6077464  6.5046286  6.3302467  6.5264184
## 156  7.3682010  7.3954185  7.2955556  7.2237326  7.1408898  7.2695149
## 157  6.5627141  6.6627305  6.3661372  6.3008297  6.4054786  6.6408307
## 158  4.5244272  4.1493909  4.7926270  4.4295693  3.7314904  3.6676934
## 159  4.0951990  3.9496816  4.1402907  3.7753488  3.5031193  3.7737382
## 160  5.2759993  5.1405241  5.3599261  5.0806896  4.5600668  4.7696064
## 161  5.6183154  5.4837208  5.6896627  5.4305237  5.2168401  5.3269585
## 162  5.1521352  4.6923199  5.5218641  5.1671988  4.3503983  4.1090194
## 163  6.6575895  6.2761806  6.9848872  6.6859446  5.9396391  5.7949340
## 164  6.8705641  6.4797527  7.2351677  6.9585621  6.1189951  5.9425795
## 165  3.8804185  3.8913928  3.8009626  3.6048814  3.6221223  3.8514027
## 166  4.2242053  4.1355020  4.2272227  3.9875753  3.8480172  4.0279501
## 167  5.3801634  4.9116253  5.7757505  5.4390254  4.4797465  4.2658985
## 168  4.1538251  4.1690373  4.0649091  3.9364594  4.0703735  4.1673202
## 169  4.0616077  3.9681892  4.0810332  3.8303666  3.5640160  3.7924537
## 170  3.9474962  3.8670101  3.9768666  3.7292295  3.4339304  3.6853489
## 171  4.1773457  4.2451763  4.0423301  3.9017499  3.9502988  4.2511933
## 172  4.0327526  4.0534718  3.9431129  3.7342679  3.7074915  4.0243011
## 173  2.4895193  2.6455780  2.1885457  2.0353246  2.5458965  2.8306709
## 174  1.9669864  1.7960757  2.1094652  1.6153633  1.2595655  1.6117276
## 175  1.8148052  1.9109365  1.6782838  1.3355481  2.0045508  2.0989629
## 176  1.6892183  1.5414640  1.9993924  1.7758152  2.2169990  1.4940411
## 177  1.3474550  1.6144048  1.2332749  1.1836539  2.1950643  1.9561366
## 178  1.6490878  1.4491990  1.8863044  1.3465632  1.3030823  1.4195917
## 179  1.9681846  1.5404880  2.3613645  1.8947803  1.1332170  0.9245312
## 180  2.1476862  1.6189254  2.6167941  2.2323325  1.8695063  1.1086021
## 181  3.1345276  2.5850466  3.6309189  3.2672390  2.1695481  1.8265232
## 182  1.9095906  1.7193330  2.0031261  1.7554304  2.1951609  1.7619029
## 183  2.7940486  2.2043011  3.2533757  2.7520366  1.6953690  1.5661488
## 184  2.3129765  1.8398846  2.6441140  2.0713808  1.3271167  1.5352607
## 185  2.2441223  2.3530424  1.9865867  1.8073401  2.4069459  2.6455628
## 186  1.4879750  1.5309910  1.4351065  1.3158225  1.9220493  1.7694059
## 187  3.7151773  3.2002899  4.2247412  3.9826596  3.3527005  2.6280592
## 188  2.9114510  2.7761847  3.1711536  3.0543068  3.1041875  2.6516590
## 189  2.8966983  2.8423204  3.1397497  3.0716772  3.3755809  2.9043586
## 190  3.1804886  2.9630169  3.5600394  3.4459305  3.2813517  2.7531361
## 191  3.4040968  3.3076408  3.7510556  3.7990141  3.9556592  3.3556572
## 192  3.0343581  2.9925479  3.3580192  3.3674961  3.5757601  3.1297199
## 193  3.4912685  3.3172264  3.9136794  3.8796257  3.8537461  3.2820499
## 194  3.5170567  3.5287810  3.7834129  3.8669331  4.2586910  3.7186988
## 195  3.3533254  3.3715442  3.6014221  3.6469594  4.0648084  3.6105677
## 196  5.4456662  5.1665417  5.8469853  5.7718226  5.4354305  4.8940948
## 197  4.9747446  4.8761307  5.2891419  5.2797478  5.1409484  4.8107294
## 198  4.8119067  4.7959500  5.0440766  5.1090414  5.0749771  4.7943409
## 199  4.9459309  4.8618167  5.2363595  5.2583562  5.1175840  4.7932809
##             91         92         93         94         95         96
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
## 92   0.2980837                                                       
## 93   2.1752304  2.2484713                                            
## 94   2.5608644  2.7092048  1.0024825                                 
## 95   2.1995107  2.1704225  0.9816738  1.8881398                      
## 96   1.0002584  1.1422761  2.3088964  2.5282934  2.5772866           
## 97   0.6964953  0.7323744  2.3196803  2.7278251  2.1868219  1.3252143
## 98   3.0545600  3.0694373  3.7319047  4.0943943  4.0067259  2.4888725
## 99   3.3334283  3.4667984  3.8012988  3.7835123  4.3658687  2.5661983
## 100  1.9235164  1.9985993  2.8330844  3.1360880  3.1563135  1.3242342
## 101  2.0027735  1.9815608  2.4677894  2.9781596  2.4110166  2.1216899
## 102  1.9451337  1.9531119  2.3510164  2.7814810  2.4332709  2.0074344
## 103  4.0510381  4.0263694  4.3619086  4.7417665  4.2088751  3.9954551
## 104  2.1390094  2.0723045  2.6697964  3.2461391  2.2606361  2.6821941
## 105  2.1278728  2.0451247  2.6837484  3.2677531  2.2795721  2.6478307
## 106  2.5643917  2.4846692  3.1119616  3.6916089  2.5681413  3.1570834
## 107  2.6417031  2.5926287  3.1566864  3.7097214  2.6351597  3.2344348
## 108  2.1704948  2.1227989  2.7132461  3.2591415  2.3357026  2.6923157
## 109  2.2153637  2.1050266  2.7876884  3.4621330  2.3598689  2.7084856
## 110  2.2822272  2.2159113  2.8232530  3.4439547  2.3664224  2.8281816
## 111  1.9775502  2.0751249  2.3177947  2.5741232  2.3555548  2.3245596
## 112  1.6942780  1.6440017  2.2231033  2.8471178  2.0555600  2.1429923
## 113  2.2584769  2.1816500  2.8065963  3.4141395  2.2485083  2.9748588
## 114  2.2809195  2.1999967  2.8303870  3.4907765  2.2571174  2.9869547
## 115  1.7857428  1.7016457  2.3538665  2.9450169  2.0099241  2.4470640
## 116  2.2215283  2.1647034  2.7494222  3.3265568  2.2520936  2.8588293
## 117  1.6546819  1.6571469  2.1504143  2.6344580  1.9407255  2.2524720
## 118  1.7832855  1.7063097  2.3163157  2.8516481  1.9593301  2.4477730
## 119  2.0748581  2.0911421  2.5365552  2.9689764  2.2272815  2.6264989
## 120  1.9675055  2.0031310  2.3705124  2.6979306  2.1444686  2.6081147
## 121  3.6232748  3.6393592  2.7426350  3.0849573  2.5307914  4.0451367
## 122  3.6530050  3.6278818  2.8656669  3.3631147  2.5018301  4.1121313
## 123  3.8729395  3.8381834  3.2045999  3.7611446  2.7232066  4.3693875
## 124  4.4350898  4.4104760  3.9160390  4.4836253  3.3567465  4.9970713
## 125  3.9244370  3.8780400  3.2854108  3.8512298  2.7642705  4.4555194
## 126  3.7071311  3.6742996  2.9667846  3.4836664  2.5647489  4.1719819
## 127  4.6814713  4.6625545  4.2043325  4.7279761  3.6386697  5.2641765
## 128  4.0681718  4.0155501  3.6849126  4.1893110  3.1864468  4.6414418
## 129  3.8648048  3.8043399  3.4511900  4.0643757  3.0270334  4.3591160
## 130  4.1552131  4.1063872  3.7747927  4.2741486  3.2630031  4.7581423
## 131  3.7563327  3.6873545  3.3055877  3.9108165  2.9211784  4.2050841
## 132  3.7287908  3.6612502  3.2625373  3.8428156  2.8767848  4.1790941
## 133  3.6935440  3.6284906  3.2130831  3.7748919  2.8774215  4.0626782
## 134  3.8693960  3.8138779  3.4240475  3.9377458  2.9628393  4.3825959
## 135  4.2961091  4.2454814  3.9376782  4.4459844  3.4661256  4.7301140
## 136  3.8977015  3.8438646  3.4814612  4.0887231  3.0327026  4.4013523
## 137  3.9283702  3.8836465  3.5076859  4.0342804  3.0538910  4.4527959
## 138  3.8466342  3.7829754  3.4254778  4.0402141  3.0095620  4.3427739
## 139  4.3126928  4.2657091  3.9796423  4.5342923  3.4431105  4.9263515
## 140  4.0119402  3.9631677  3.6313274  4.2097062  3.1570396  4.5487494
## 141  4.3795583  4.3546116  4.0405842  4.6089217  3.5545345  4.9607430
## 142  5.6411782  5.6277084  5.4391975  5.8805226  4.8625312  6.2668312
## 143  6.8164989  6.7923559  6.8665947  7.2093657  6.4943006  7.4323801
## 144  5.4782612  5.4504821  5.5354485  5.9487226  5.0870074  6.1950489
## 145  5.9599975  5.9370281  6.0213140  6.3831123  5.5408355  6.7154880
## 146  5.9407660  5.9246990  6.0044516  6.4563401  5.6284898  6.4521207
## 147  5.5038589  5.4623584  5.5483556  5.9164436  5.2136951  5.9844878
## 148  5.8883291  5.8727092  5.9412528  6.2894997  5.4791539  6.6150556
## 149  5.6355359  5.6261414  5.6790208  6.0328282  5.2533361  6.3046177
## 150  5.1201374  5.0903535  5.1524110  5.5443507  4.7618916  5.7953691
## 151  4.6640085  4.6185212  4.6731326  5.0793286  4.3884193  5.2373186
## 152  4.9076776  4.8516645  4.9344678  5.2771425  4.5863362  5.5103179
## 153  6.4001897  6.3673854  6.3939124  6.5871470  6.1526709  6.9153623
## 154  5.0212369  4.9793635  5.0507108  5.4247773  4.7233611  5.5481547
## 155  6.1808506  6.1468821  6.1891389  6.5199780  5.9576265  6.6408971
## 156  6.9434069  6.9362714  6.9321862  7.1820893  6.7898159  7.2164454
## 157  6.0432716  6.0121352  6.0714355  6.3628552  5.7702279  6.4664033
## 158  4.0100478  3.9689525  3.8277304  4.2047431  3.8341687  3.9597873
## 159  3.4344137  3.3435716  3.2775183  3.7549595  2.9752160  3.8234282
## 160  4.6090854  4.5447661  4.5998258  5.0051284  4.4119090  5.0733072
## 161  5.1937443  5.1511994  5.0622579  5.3380162  4.9564085  5.3767153
## 162  4.7596645  4.7470448  4.5602222  4.8238318  4.7338717  4.5047606
## 163  6.3353141  6.3154884  6.2012682  6.4570571  6.3125509  6.1476155
## 164  6.5790765  6.5711319  6.4354579  6.7103246  6.5865652  6.3605002
## 165  3.3391315  3.2823537  3.1311011  3.5940118  2.7661077  3.8544121
## 166  3.6857673  3.6382995  3.5113995  3.9426119  3.2657903  3.9230500
## 167  4.9873189  4.9716584  4.8140165  5.1526113  4.9624545  4.7290819
## 168  3.7124602  3.7064994  3.4862735  3.8130981  3.2956984  3.9651976
## 169  3.4641331  3.4054523  3.2971353  3.8239552  2.9955556  3.8029658
## 170  3.3525909  3.2911553  3.1663535  3.7255621  2.8518463  3.7521082
## 171  3.6365087  3.5804032  3.4845096  3.9947324  3.0546535  4.1343231
## 172  3.4531451  3.3786020  3.2901537  3.8116866  2.8550967  3.9838818
## 173  1.8193857  1.7501756  2.9856503  3.4306940  2.5441883  2.5086827
## 174  0.9794205  0.8439498  2.4858148  3.0156027  2.2866228  1.6035822
## 175  1.0856165  1.0993566  2.4451260  2.7400902  2.3247547  1.7597601
## 176  1.6383096  1.8554007  2.4542618  2.3042849  2.9845468  1.3722431
## 177  1.1606736  1.3520857  2.2890194  2.3633564  2.4667630  1.5753744
## 178  0.8742291  0.8194090  2.3250781  2.7016552  2.3126408  1.3214565
## 179  1.2972979  1.2994593  2.5271553  2.9390889  2.6298401  1.2612393
## 180  1.9429630  2.0391875  2.9129086  3.0567148  3.2614686  1.3819739
## 181  2.8022606  2.8073801  3.6521496  4.0678942  3.8097754  2.3894514
## 182  1.6321174  1.7386288  2.7852496  2.9081879  2.9238315  1.4612795
## 183  2.3062692  2.2473731  3.3319754  3.7657523  3.3802982  1.9748647
## 184  1.6582355  1.5260738  2.9530703  3.4337195  2.8293426  1.6464002
## 185  1.7281342  1.6574536  3.0156041  3.4415275  2.6189131  2.2582342
## 186  1.1624154  1.2565406  2.5736611  2.8909090  2.5170757  1.4027642
## 187  3.7066738  3.7983412  4.2441733  4.3231113  4.6776534  3.0247069
## 188  2.8920554  3.0074398  2.7224518  2.7186257  3.1667490  2.6035735
## 189  3.0490706  3.1819157  2.7850683  2.5935985  3.3195751  2.7460100
## 190  3.2713071  3.3844379  3.0630297  3.0590373  3.5696720  2.8472524
## 191  3.8058778  3.9494580  3.4836627  3.2691442  4.0680120  3.3022390
## 192  3.3917735  3.5097370  3.0818354  2.9526417  3.5872775  3.0418934
## 193  3.8426508  3.9660983  3.5333168  3.3767747  4.1184439  3.3307388
## 194  3.9837438  4.1369308  3.4617768  3.1548981  4.0798659  3.5956545
## 195  3.7762332  3.9090563  3.2685188  3.0131413  3.8235721  3.4281910
## 196  5.6217804  5.7169975  5.2491447  5.1778961  5.7396913  5.0748611
## 197  5.1867393  5.2631640  4.7449280  4.7186164  5.1324891  4.8706942
## 198  5.0217813  5.1028194  4.5927290  4.6195746  4.9046314  4.7633368
## 199  5.1518280  5.2285174  4.7271516  4.7410801  5.0737960  4.8435528
##             97         98         99        100        101        102
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
## 92                                                                   
## 93                                                                   
## 94                                                                   
## 95                                                                   
## 96                                                                   
## 97                                                                   
## 98   3.4566989                                                       
## 99   3.7453129  1.5401119                                            
## 100  2.3266353  1.2362434  1.6192694                                 
## 101  2.1984578  3.0372468  3.4795956  2.3398246                      
## 102  2.2064401  2.9833996  3.3266190  2.2374529  0.4154576           
## 103  4.0576614  5.2561221  5.6186495  4.6862626  3.7156696  3.7559685
## 104  2.0258014  4.1723934  4.6396282  3.3128630  1.3743744  1.5613327
## 105  2.0616624  4.0799921  4.5743455  3.2512492  1.2675374  1.4692751
## 106  2.3545150  4.6554197  5.1450039  3.8196888  1.9348090  2.1888248
## 107  2.3952126  4.7613054  5.1995794  3.9004954  2.0720224  2.3208148
## 108  2.0790948  4.1809640  4.6096241  3.3223023  1.3752036  1.5771084
## 109  2.2088790  3.8590925  4.4964460  3.1363373  1.1790274  1.4202253
## 110  2.1499059  4.2081310  4.7256562  3.3906722  1.4798433  1.7190146
## 111  1.9725187  4.0221276  4.0981812  3.0197317  1.4294049  1.3738405
## 112  1.9824742  3.2427622  3.7602988  2.4744416  1.5880288  1.6361430
## 113  2.1401475  4.5282001  5.0068794  3.6586015  2.3745827  2.5586661
## 114  2.1722516  4.4164534  4.9530229  3.5865526  2.3335145  2.5336529
## 115  1.9173497  3.9531736  4.4230968  3.0858244  1.9401525  2.0027732
## 116  2.1161041  4.5279044  4.9624613  3.6376099  2.3943876  2.5493575
## 117  1.7554476  3.8934429  4.1928171  2.9455439  1.8794482  1.9229293
## 118  1.8406069  4.1023041  4.5042925  3.1867540  2.0229455  2.0840465
## 119  2.0046773  4.4450747  4.6976484  3.4827589  2.3390847  2.4383384
## 120  1.8989784  4.5228233  4.6876934  3.4897400  2.3804116  2.4151087
## 121  3.6904310  5.3323579  5.4980387  4.5792415  3.3417463  3.3963273
## 122  3.7172514  5.2959197  5.6205614  4.6058717  3.3032723  3.3941098
## 123  3.8747602  5.5112247  5.9000657  4.8444624  3.4910702  3.6408992
## 124  4.3280473  6.1843727  6.5992241  5.4960619  4.1259209  4.3183459
## 125  3.9123590  5.6434615  6.0569451  4.9630511  3.5754955  3.7245155
## 126  3.7649772  5.3071163  5.6570845  4.6403588  3.3179238  3.4326680
## 127  4.5325657  6.5683177  6.9493527  5.8361865  4.4434278  4.6357148
## 128  4.0226644  5.9241793  6.3308873  5.2044473  3.1812565  3.3422109
## 129  3.9406558  5.2396079  5.7619652  4.6760662  2.7050894  2.8607866
## 130  4.0801812  6.0916514  6.4938560  5.3451505  3.3416910  3.4968249
## 131  3.8709279  5.0428088  5.5675448  4.5043970  2.5348914  2.6673929
## 132  3.8299679  5.0884237  5.5815531  4.5212007  2.5312098  2.6608878
## 133  3.8278090  4.8806958  5.3573091  4.3621927  2.3938644  2.5298130
## 134  3.8593446  5.5966445  6.0046132  4.9079074  2.8804319  3.0308507
## 135  4.2415266  6.0669512  6.4857592  5.3817309  3.4766095  3.6297879
## 136  3.9348301  5.3440988  5.8460138  4.7527359  2.7763703  2.9467005
## 137  3.9206247  5.6433980  6.0558651  4.9588822  2.9459257  3.1023643
## 138  3.9322548  5.2310680  5.7602729  4.6656741  2.7005200  2.8405563
## 139  4.2320361  6.1533340  6.6093581  5.4465458  3.4795632  3.6590085
## 140  4.0153420  5.5825246  6.0532190  4.9539056  2.9644865  3.1476581
## 141  4.3134831  6.0579443  6.5090932  5.3900326  3.5065559  3.6908002
## 142  5.3877026  7.6568163  7.9987832  6.8848446  5.0833797  5.3176111
## 143  6.8515755  8.4773094  8.8055491  7.8814109  6.9594126  7.0884981
## 144  5.5355172  7.3517919  7.7144553  6.6926018  5.6270615  5.7866295
## 145  5.9339716  8.0854426  8.4011998  7.3367495  6.1908104  6.3507070
## 146  6.0332036  7.4892991  7.8924100  6.9454532  6.0360363  6.1809826
## 147  5.6588485  7.1929944  7.5454088  6.6076069  5.6691154  5.7700826
## 148  5.8685740  7.9615956  8.2506049  7.2232063  6.1001432  6.2646416
## 149  5.6574593  7.5744084  7.8541416  6.8769543  5.8075644  5.9716537
## 150  5.2430640  6.9806828  7.3268143  6.3243578  5.2984707  5.4234544
## 151  4.9432058  6.0833355  6.4669509  5.5774290  4.7265437  4.8217123
## 152  5.1024351  6.6852822  7.0166080  6.0665190  5.0730647  5.1735948
## 153  6.5272618  8.1189048  8.3286871  7.4907077  6.6371660  6.6876545
## 154  5.2173845  6.6654971  7.0108255  6.0888641  5.1524582  5.2594053
## 155  6.3755188  7.4414281  7.7842283  6.9846308  6.2749476  6.3421480
## 156  7.1235315  8.1448776  8.3808845  7.6929955  7.0797797  7.1192158
## 157  6.1538870  7.8365081  8.1164874  7.2042223  6.2774023  6.3578819
## 158  4.3956552  3.8477636  4.2217873  3.7939612  3.8521006  3.9214363
## 159  3.6697330  4.8125188  5.2572820  4.2619517  3.6712888  3.7411501
## 160  4.9991098  5.6498540  6.0828133  5.2815590  4.6074324  4.6571568
## 161  5.3908929  6.0089597  6.2992425  5.6364300  5.3300604  5.3598449
## 162  5.1990353  3.7459469  3.9796982  4.0242177  4.4747122  4.5059383
## 163  6.6886120  5.4072025  5.6663236  5.6978955  6.0703318  6.1015941
## 164  6.9536117  5.3750237  5.6522369  5.7774763  6.2779312  6.2980939
## 165  3.4633038  5.0515779  5.4158997  4.3669999  3.6758492  3.7665756
## 166  3.8640500  5.0263358  5.3849153  4.4668557  3.9302218  4.0073280
## 167  5.4261803  3.6766592  4.0430652  4.1080222  4.6331934  4.6799520
## 168  3.8379228  5.3078504  5.5236283  4.6325606  4.0645417  4.1243079
## 169  3.6633826  4.7752014  5.2234215  4.2327932  3.6781565  3.7703227
## 170  3.5583635  4.6960348  5.1713089  4.1404952  3.5869705  3.6718810
## 171  3.6920303  5.4791474  5.8955078  4.7767060  4.0095775  4.1101619
## 172  3.5508003  5.2422618  5.6806568  4.5597602  3.8070942  3.9032074
## 173  1.5786668  4.3513699  4.7080088  3.3823650  2.8695489  3.0182666
## 174  1.2705580  3.1349188  3.6431445  2.2181646  2.2499017  2.2978300
## 175  1.1394334  3.8263673  4.0172035  2.7493052  2.5745157  2.5786953
## 176  2.0898505  2.9994192  2.5967079  1.9332453  2.8086762  2.6148271
## 177  1.2798117  3.7377555  3.6670973  2.5735611  2.7173002  2.6305198
## 178  1.2606625  3.0947134  3.4168067  2.0932105  2.3263309  2.2870827
## 179  1.7945841  2.2355073  2.6676767  1.3849065  2.2198422  2.1983476
## 180  2.3977319  1.8273823  1.7542450  1.0617676  2.5410964  2.4564480
## 181  3.2021980  1.0115621  1.9388899  1.3707315  2.8824159  2.9140831
## 182  1.8220873  2.9910608  2.9064562  2.0444661  2.4981948  2.5239906
## 183  2.6905572  1.6085735  2.3970318  1.4485880  2.5517432  2.6058295
## 184  1.9405687  2.4650611  3.1061476  1.8352505  2.2784640  2.3662851
## 185  1.4297523  4.0837622  4.4326104  3.1298949  2.7141084  2.8774630
## 186  1.1310386  3.2366431  3.3938427  2.1937039  2.3379743  2.4109558
## 187  4.1213636  1.6390795  1.1169602  2.0670586  3.7558260  3.6936086
## 188  3.1023920  3.4077490  3.1795390  2.7356739  3.7755843  3.6682579
## 189  3.2305813  3.8319741  3.4600076  3.0703414  4.0388604  3.8832509
## 190  3.5306598  3.1347243  2.8518409  2.6769628  3.9957945  3.8708514
## 191  3.9875810  3.7990788  3.2419361  3.2948897  4.5493410  4.3992131
## 192  3.5323105  3.8763019  3.5482495  3.2235998  4.2911217  4.1393646
## 193  4.0716800  3.5897987  3.1133988  3.1889151  4.5431732  4.3796990
## 194  4.1105391  4.3768518  3.8287256  3.7447917  4.9444257  4.7693688
## 195  3.8745713  4.3930519  3.9614679  3.7068411  4.7990435  4.6344146
## 196  5.8801300  4.4576055  4.0383151  4.5772958  6.1411326  6.0483954
## 197  5.3284510  5.0330318  4.8401539  4.7613985  6.1331289  6.0233913
## 198  5.0953802  5.1765971  5.0397443  4.7962241  6.0279199  5.9450656
## 199  5.2692917  4.9921161  4.8292327  4.7266548  6.0758456  5.9901485
##            103        104        105        106        107        108
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
## 92                                                                   
## 93                                                                   
## 94                                                                   
## 95                                                                   
## 96                                                                   
## 97                                                                   
## 98                                                                   
## 99                                                                   
## 100                                                                  
## 101                                                                  
## 102                                                                  
## 103                                                                  
## 104  3.5889425                                                       
## 105  3.5603010  0.2489707                                            
## 106  3.7525203  0.7340124  0.7885177                                 
## 107  3.8344691  0.8951573  1.0136634  0.3554763                      
## 108  3.5436105  0.3370811  0.3423965  0.6684111  0.8103982           
## 109  3.5915773  0.6298186  0.5064419  1.0758868  1.2928956  0.7214010
## 110  3.5934530  0.3613525  0.4718651  0.6235519  0.7286414  0.4027015
## 111  3.7443760  1.2059200  1.2918729  1.7008194  1.6716288  1.1622391
## 112  3.9148934  1.8218766  1.7706988  2.2420474  2.3531494  1.8461569
## 113  4.0065238  1.6020089  1.6437046  1.5134579  1.5443650  1.5962379
## 114  4.0189288  1.6127562  1.6628768  1.5567517  1.5727582  1.6245628
## 115  3.8036913  1.5869813  1.5520825  1.8710224  2.0030542  1.6075595
## 116  3.5015262  1.6611066  1.7049191  1.6407562  1.6683702  1.6394523
## 117  3.8932736  1.6150267  1.6333522  1.9244110  1.9768152  1.6214452
## 118  3.8899054  1.5791494  1.5718540  1.8420680  1.9643708  1.6331871
## 119  3.4796861  1.7658393  1.8204424  1.8385355  1.8222364  1.7057146
## 120  4.0247967  1.7893142  1.8629453  1.9449125  1.9329016  1.7827285
## 121  4.7068109  3.0559721  3.0782926  3.1200089  3.1161050  3.0196842
## 122  4.5416039  2.9689459  2.9758507  3.0049297  3.0337678  2.9481423
## 123  4.6499166  3.0462777  3.0674848  2.9618041  2.9565310  3.0127294
## 124  4.9624739  3.4615636  3.5301567  3.2161322  3.1181375  3.4116866
## 125  4.6720378  3.0575923  3.0783541  2.9505825  2.9560482  3.0318473
## 126  4.6272226  2.9849427  2.9839298  2.9796915  3.0106432  2.9538270
## 127  5.0756694  3.6797460  3.7603981  3.3747173  3.2542574  3.6203758
## 128  4.4014958  2.4059343  2.4384994  2.2194327  2.2333613  2.3802744
## 129  4.2815008  2.3087513  2.2962998  2.3387418  2.4004255  2.2948724
## 130  4.5040795  2.4861249  2.5433358  2.2826459  2.2678310  2.4756716
## 131  4.2097813  2.2764530  2.2397710  2.4000348  2.5062572  2.2888132
## 132  4.2184671  2.2371785  2.2053370  2.3538163  2.4616008  2.2568276
## 133  4.1331291  2.2968444  2.2393600  2.4478620  2.5722560  2.3028323
## 134  4.2479546  2.2518559  2.2738070  2.1919671  2.2410013  2.2637288
## 135  3.3491519  2.7808065  2.8113550  2.6491564  2.6694679  2.7529348
## 136  4.2879176  2.2984219  2.3122435  2.2847222  2.3132132  2.2903165
## 137  4.1814558  2.2959746  2.3233473  2.1983049  2.2138771  2.2685628
## 138  4.2393943  2.3066502  2.2910939  2.3675681  2.4417800  2.3031914
## 139  4.5528506  2.6285039  2.6927990  2.3821946  2.3290385  2.5967493
## 140  4.3882580  2.3709706  2.3922599  2.2482764  2.2498877  2.3302928
## 141  4.5931907  2.7619550  2.8396236  2.5520253  2.4466634  2.7088117
## 142  5.7725421  4.0922171  4.2073576  3.5886876  3.3885470  4.0179250
## 143  7.5205443  6.4228748  6.4682648  6.2216314  6.1637071  6.3920314
## 144  6.3526847  5.0129772  5.0657282  4.7669852  4.6946776  4.9715272
## 145  6.7362848  5.4124412  5.4858742  5.0933049  4.9954555  5.3712898
## 146  5.3044710  5.5590631  5.5991482  5.3930236  5.3301758  5.4919559
## 147  4.8801532  5.2457838  5.2457614  5.1439780  5.1682522  5.1974393
## 148  6.6708948  5.3650265  5.4373229  5.0492601  4.9457295  5.3170885
## 149  6.2782373  5.1737615  5.2355185  4.8958270  4.8001405  5.1151874
## 150  5.8054768  4.7636161  4.7981355  4.6011702  4.5687121  4.7266436
## 151  5.6469056  4.5293871  4.5110504  4.5183791  4.5605965  4.5037967
## 152  5.6144877  4.6799631  4.6678618  4.5828876  4.6324072  4.6549925
## 153  6.9839666  6.2336743  6.2374089  6.1603292  6.1915488  6.2202401
## 154  5.1380475  4.7990679  4.7932449  4.7143568  4.7428967  4.7564139
## 155  6.6282084  6.0463789  6.0435874  6.0355680  6.0599216  6.0300888
## 156  6.0406446  6.8804109  6.8787837  6.8955871  6.9122989  6.8361751
## 157  4.8925156  5.8003154  5.8091649  5.6955652  5.7148914  5.7530192
## 158  5.4178833  4.5077779  4.3925872  4.7196501  4.8495602  4.4613077
## 159  4.7331798  3.6364626  3.5595046  3.7322700  3.8732884  3.6240716
## 160  5.5934213  4.6573379  4.5988589  4.7755055  4.8803649  4.6518580
## 161  6.0931796  5.4226652  5.3651718  5.5322275  5.6288036  5.4057056
## 162  6.1778216  5.3921408  5.2683384  5.6695494  5.7945553  5.3417145
## 163  7.5145963  6.8177401  6.7156463  7.0525186  7.1591825  6.7847911
## 164  7.7257590  7.0907878  6.9951471  7.3598003  7.4525227  7.0586516
## 165  4.9911054  3.4343095  3.4182985  3.4675710  3.5339318  3.4359554
## 166  3.9587264  3.8749842  3.8290338  3.9569592  4.0465927  3.8396190
## 167  6.2941721  5.5819667  5.4629858  5.8649056  5.9792189  5.5342167
## 168  3.9131232  3.9013158  3.8883820  3.9611717  4.0033350  3.8534078
## 169  4.2547646  3.6226843  3.5778014  3.7083941  3.7942999  3.5941135
## 170  4.4498272  3.5153870  3.4791419  3.6239103  3.7056577  3.5044073
## 171  4.2692167  3.5893965  3.5957501  3.5712668  3.6131705  3.5790651
## 172  4.6283396  3.4598842  3.4471092  3.4725134  3.5464694  3.4658645
## 173  4.4044987  2.3474845  2.3668214  2.2737745  2.3041075  2.3342957
## 174  4.2018437  2.3298613  2.2795279  2.6175179  2.7334525  2.3491120
## 175  4.2772618  2.3806394  2.3781543  2.5990656  2.6649237  2.3814478
## 176  4.7346846  3.3547101  3.3364869  3.8172265  3.8573574  3.3365164
## 177  4.4370402  2.6984085  2.7410213  3.0389932  3.0415530  2.7152644
## 178  4.2883486  2.5270116  2.4872739  2.9067325  3.0229729  2.5760141
## 179  4.3977524  2.8463868  2.7752346  3.2500183  3.3561242  2.8480227
## 180  4.8279370  3.4541023  3.3752450  3.8822585  3.9685855  3.4205698
## 181  5.1146206  3.9103864  3.8134066  4.2920008  4.3859543  3.8824133
## 182  4.6393037  2.9578138  2.9098269  3.2014455  3.2487366  2.8908890
## 183  4.8021001  3.4539801  3.3327759  3.8036624  3.9486332  3.4413492
## 184  4.4680861  2.8199943  2.7091705  3.1125981  3.2765090  2.8323752
## 185  4.3400613  2.3360713  2.3434832  2.3018740  2.3452330  2.3304982
## 186  4.2851278  2.4548174  2.4641819  2.6757520  2.6831322  2.4321306
## 187  5.8766469  4.9284718  4.8434258  5.3516619  5.4172445  4.8827463
## 188  5.4505368  4.2828989  4.2705859  4.6640686  4.6930669  4.2841021
## 189  5.5172214  4.4739861  4.4794235  4.8909446  4.9176570  4.5002631
## 190  5.7362973  4.6741286  4.6584318  5.1117116  5.1450805  4.6938444
## 191  6.0487636  5.1820521  5.2002596  5.6409394  5.6462345  5.2311458
## 192  5.7867048  4.7637554  4.7913811  5.2226984  5.2408682  4.8421768
## 193  6.1429907  5.2426577  5.2473935  5.7333636  5.7610534  5.3033781
## 194  6.3463875  5.4151731  5.4486940  5.8612536  5.8546174  5.4658839
## 195  6.0658868  5.1946284  5.2264849  5.6270192  5.6341664  5.2553671
## 196  7.6657640  6.9795720  6.9484100  7.3804001  7.4114149  6.9887204
## 197  7.3862925  6.6185722  6.6343463  7.0166541  7.0361590  6.6914293
## 198  6.9893652  6.3835439  6.4187172  6.7366094  6.7307367  6.4512959
## 199  7.3191768  6.5457473  6.5661137  6.9175588  6.9253506  6.6131019
##            109        110        111        112        113        114
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
## 92                                                                   
## 93                                                                   
## 94                                                                   
## 95                                                                   
## 96                                                                   
## 97                                                                   
## 98                                                                   
## 99                                                                   
## 100                                                                  
## 101                                                                  
## 102                                                                  
## 103                                                                  
## 104                                                                  
## 105                                                                  
## 106                                                                  
## 107                                                                  
## 108                                                                  
## 109                                                                  
## 110  0.6191934                                                       
## 111  1.5934552  1.3837169                                            
## 112  1.6946109  1.8845019  1.9749290                                 
## 113  1.7947344  1.5724363  2.1488971  1.5474892                      
## 114  1.7367175  1.5362576  2.1987598  1.4735112  0.3118082           
## 115  1.6274852  1.6870346  1.9193785  0.8395774  0.9947311  1.0506072
## 116  1.8753851  1.6470366  2.1027220  1.5756129  0.5817520  0.6945837
## 117  1.7977305  1.7259807  1.6368780  0.8909781  1.0520214  1.1221679
## 118  1.7399392  1.7251853  1.8777091  1.0638419  0.9377574  1.0647806
## 119  2.0693769  1.8058055  1.8460360  1.5904059  0.9624578  1.1074477
## 120  2.1702576  1.9192706  1.7037917  1.6378486  1.0997958  1.2924422
## 121  3.2383420  3.1010624  3.0423352  3.1584754  2.9711355  3.0306404
## 122  3.0719683  2.9837814  3.1612048  3.0787296  2.8648354  2.8959393
## 123  3.1459360  2.9980381  3.3550861  3.2596987  2.8456989  2.8524441
## 124  3.6065246  3.3259879  3.8260237  3.8550055  3.1266235  3.1007661
## 125  3.1623556  3.0146069  3.4175332  3.3201124  2.8384938  2.8550242
## 126  3.0718349  2.9843433  3.2257679  3.1068054  2.8542763  2.8827434
## 127  3.8747584  3.5428477  4.0327622  4.1639672  3.2991257  3.2956913
## 128  2.5830856  2.3719881  2.8861750  3.1625962  2.4984994  2.5476065
## 129  2.2442091  2.2397321  2.7926785  2.7341346  2.5759553  2.5283060
## 130  2.6968537  2.4451581  2.9584215  3.2886736  2.5469169  2.5920059
## 131  2.1785614  2.2599271  2.7436465  2.6101919  2.6225886  2.5860485
## 132  2.1861139  2.2427243  2.6928255  2.6182308  2.5818427  2.5641820
## 133  2.2129796  2.3160476  2.7035459  2.5680709  2.6736650  2.6593682
## 134  2.3990704  2.2559403  2.7110753  2.9199548  2.4540862  2.4903635
## 135  2.9290893  2.7306403  3.2328129  3.4558657  2.8807971  2.9136459
## 136  2.2900533  2.2138065  2.7815647  2.8006973  2.5276858  2.4778384
## 137  2.4237320  2.2504307  2.7322103  2.9556091  2.4622541  2.4797552
## 138  2.2325821  2.2518706  2.7903853  2.7164522  2.5951902  2.5497253
## 139  2.7791452  2.5140603  3.1359899  3.3970523  2.6417447  2.6372277
## 140  2.4202092  2.2706107  2.8548350  2.9696575  2.5152169  2.4894656
## 141  2.8702793  2.5926207  3.1790302  3.4288964  2.7822234  2.7251467
## 142  4.3842483  3.9180658  4.4937157  4.9957653  3.8192754  3.8372312
## 143  6.5465132  6.3509266  6.6741437  6.1898544  5.5569128  5.5680966
## 144  5.1588339  4.9214196  5.3172742  4.6700140  3.8601690  3.8713310
## 145  5.6363696  5.3277510  5.7140914  5.2861184  4.2676332  4.3155379
## 146  5.6219239  5.4282371  5.8274656  5.1394325  4.5963668  4.5595715
## 147  5.3278611  5.2145296  5.5130357  4.7563616  4.3051677  4.3525208
## 148  5.5919774  5.2786685  5.6390702  5.2104401  4.2162872  4.2634028
## 149  5.3728742  5.0833892  5.4176895  4.9077738  4.0259291  4.0608754
## 150  4.8906480  4.7085740  5.0287484  4.2873695  3.6344098  3.6632842
## 151  4.5345622  4.5159674  4.7659687  3.6814394  3.5151134  3.5247616
## 152  4.7801683  4.6977315  4.9579640  4.0889780  3.6220436  3.7056601
## 153  6.3745174  6.2766183  6.3916690  5.8842167  5.4739235  5.5646191
## 154  4.8720706  4.7781507  5.0547659  4.1804198  3.7797674  3.8253489
## 155  6.0624748  6.0285602  6.2373265  5.4845172  5.3185109  5.3221338
## 156  6.9203289  6.8609035  6.9708689  6.3861691  6.2690026  6.2857512
## 157  5.9324622  5.7886779  6.0176004  5.4462544  4.9489155  5.0226597
## 158  4.3135681  4.5436820  4.5865126  3.1064555  3.9094328  3.8875959
## 159  3.5939604  3.7043143  3.9192457  2.5079860  2.6337155  2.7012496
## 160  4.5642665  4.6856117  4.8784057  3.5848775  3.8237240  3.8233271
## 161  5.3815607  5.4742999  5.5414937  4.6468984  4.8506509  4.8830762
## 162  5.1531017  5.4306029  5.3451584  3.9926779  5.0053988  4.9633386
## 163  6.5854357  6.8345522  6.8209865  5.7224049  6.5292876  6.4744000
## 164  6.8240598  7.0872729  7.0604736  5.9430967  6.8466071  6.7613839
## 165  3.5091698  3.4791524  3.6704081  2.4581276  2.2247090  2.2916089
## 166  3.8820197  3.9033219  4.0672046  2.8841297  2.9326999  2.9778557
## 167  5.2921454  5.5854079  5.5706806  4.1630608  5.2212657  5.1396049
## 168  4.0071856  3.9331010  3.9684025  3.0408720  2.9237758  2.9963304
## 169  3.5837167  3.6277359  3.8684236  2.4912762  2.5829439  2.5893261
## 170  3.4682242  3.5207170  3.7678633  2.3194354  2.4443666  2.4315034
## 171  3.6761624  3.5864421  3.8873110  2.8187948  2.3797163  2.4236344
## 172  3.5193033  3.4864650  3.7817122  2.5687964  2.2334085  2.2889814
## 173  2.5784790  2.3920254  2.6455605  2.2226018  1.5381480  1.6668967
## 174  2.2941043  2.4158185  2.4947900  1.4316592  1.9334996  1.9389011
## 175  2.5858157  2.5270329  2.3186762  1.8786005  1.9021652  2.0281473
## 176  3.4617449  3.5255795  2.7134952  2.4241475  3.3077963  3.3602491
## 177  2.9546345  2.8585018  2.2608142  2.1157555  2.4024547  2.4892202
## 178  2.5627172  2.6852696  2.4880902  1.6314557  2.2743578  2.3179296
## 179  2.7259939  2.9351766  2.7536405  1.6592513  2.7016160  2.6693399
## 180  3.3620317  3.5621637  3.0996093  2.7189206  3.7294976  3.7197918
## 181  3.6133280  3.9109363  3.8413073  3.0638360  4.1688072  4.0629747
## 182  3.0584748  3.0662225  2.6604203  2.6210358  3.0638253  3.1245290
## 183  3.1940305  3.5076008  3.5129162  2.7183059  3.6891106  3.6357629
## 184  2.6590676  2.9100926  3.0171284  2.3252633  2.9855961  2.9789672
## 185  2.5492652  2.3917257  2.6142092  2.5785379  2.1630232  2.2496071
## 186  2.6065521  2.5231928  2.3064224  2.2932606  2.4926417  2.5183721
## 187  4.7420859  4.9820117  4.5407846  4.0694865  5.2329065  5.1714898
## 188  4.3207481  4.3918955  3.8627587  3.2608875  4.0322431  4.0357987
## 189  4.5797739  4.6252493  3.9637659  3.5476406  4.2692277  4.3010823
## 190  4.6563560  4.7776214  4.2354421  3.5732440  4.5233168  4.4935917
## 191  5.2575599  5.3137928  4.6225180  4.2300904  5.0858747  5.0728304
## 192  4.8578943  4.9116790  4.2891006  3.8532861  4.6206696  4.6158788
## 193  5.2677016  5.3789839  4.7269986  4.2217898  5.1837213  5.1587897
## 194  5.5347044  5.5575629  4.8220181  4.7200291  5.4327146  5.4377131
## 195  5.3234939  5.3460103  4.6687948  4.5403026  5.1886321  5.2045881
## 196  6.9009969  7.0531520  6.5680134  6.0059462  6.9543163  6.9038661
## 197  6.6276096  6.7166766  6.2819757  5.6170095  6.3460118  6.3056321
## 198  6.4269046  6.4575605  6.0742326  5.4585253  6.0411313  5.9963011
## 199  6.5561789  6.6259110  6.2310812  5.5591775  6.2436394  6.1945704
##            115        116        117        118        119        120
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
## 92                                                                   
## 93                                                                   
## 94                                                                   
## 95                                                                   
## 96                                                                   
## 97                                                                   
## 98                                                                   
## 99                                                                   
## 100                                                                  
## 101                                                                  
## 102                                                                  
## 103                                                                  
## 104                                                                  
## 105                                                                  
## 106                                                                  
## 107                                                                  
## 108                                                                  
## 109                                                                  
## 110                                                                  
## 111                                                                  
## 112                                                                  
## 113                                                                  
## 114                                                                  
## 115                                                                  
## 116  1.0143920                                                       
## 117  0.6114966  1.0504785                                            
## 118  0.4216386  0.9821804  0.5332130                                 
## 119  1.1316964  0.5950068  0.8863748  1.0349129                      
## 120  1.1273699  1.0625079  0.7483175  0.8766647  0.7398350           
## 121  2.9935444  2.9722020  2.8839318  2.9465858  2.8866347  2.8584412
## 122  2.9013190  2.8669810  2.8950337  2.8948491  2.8919672  2.9440404
## 123  3.0635014  2.8800614  3.0621972  3.0634281  2.9684544  3.0875683
## 124  3.5982118  3.1678520  3.5782469  3.6060230  3.3086655  3.4986110
## 125  3.0705573  2.8786074  3.1026159  3.0666461  2.9961320  3.1039731
## 126  2.9339928  2.8865343  2.9368273  2.9310817  2.9329054  2.9966448
## 127  3.8395823  3.3214856  3.8104957  3.8285311  3.4537474  3.6474983
## 128  2.7888950  2.5712492  2.8541128  2.7659557  2.7223303  2.7817723
## 129  2.6128971  2.6530139  2.7382652  2.7120769  2.8288902  2.9437892
## 130  2.8866147  2.6246240  2.9407605  2.8523706  2.7829388  2.8211032
## 131  2.5344394  2.6847543  2.6720366  2.6222023  2.8416450  2.9289887
## 132  2.5104494  2.6461369  2.6273377  2.5652110  2.7876670  2.8494593
## 133  2.5452961  2.7144971  2.6369534  2.5963070  2.8198448  2.9110572
## 134  2.6303793  2.5078692  2.6762607  2.5914268  2.6351067  2.6828275
## 135  3.1068997  2.6656553  3.1883193  3.1083082  2.8009540  3.1336068
## 136  2.6580632  2.6034411  2.7427409  2.7285479  2.7769411  2.8998551
## 137  2.6700864  2.4940835  2.7241048  2.6804747  2.6259136  2.7348299
## 138  2.5877491  2.6591927  2.7322582  2.6926752  2.8378520  2.9452060
## 139  3.0402446  2.7216670  3.1114533  3.0623934  2.9216633  3.0375316
## 140  2.7515028  2.6065763  2.8246559  2.8078671  2.7782393  2.9032561
## 141  3.1787150  2.8476637  3.2095603  3.2470294  3.0228390  3.1920309
## 142  4.5836418  3.9242495  4.5159399  4.5236798  4.0697420  4.2082763
## 143  5.9197940  5.6148613  5.9255420  5.9040605  5.7195315  5.7916821
## 144  4.3479392  3.9443402  4.3426553  4.3267749  4.0796880  4.1868095
## 145  4.8546662  4.3460952  4.8327703  4.7892226  4.4714764  4.5410526
## 146  4.9175320  4.3656211  4.9615808  4.9970237  4.4794949  4.9213211
## 147  4.4470644  4.0340165  4.5405283  4.4697608  4.1110020  4.4808651
## 148  4.8089351  4.2891124  4.7588118  4.7376012  4.3912234  4.4745901
## 149  4.5669045  4.0478872  4.5052800  4.5151017  4.1265132  4.2789387
## 150  3.9669608  3.6280330  3.9910236  3.9580175  3.7346115  3.8748103
## 151  3.5538652  3.5351189  3.6172077  3.5876114  3.6203347  3.7276823
## 152  3.7680301  3.5952540  3.8363128  3.7212770  3.6756496  3.7730767
## 153  5.5706077  5.4406227  5.6047825  5.5064523  5.4622697  5.4665754
## 154  3.9190763  3.6249254  3.9833811  3.9258201  3.6966831  3.9635552
## 155  5.3525217  5.2676958  5.4147699  5.3865553  5.3357573  5.4617628
## 156  6.2414972  5.9819168  6.2920658  6.2956285  5.9765141  6.3037834
## 157  5.0842969  4.6003194  5.1607338  5.0787271  4.6340309  5.0223341
## 158  3.5235315  3.9137530  3.5235836  3.6060586  3.8694207  4.0220401
## 159  2.3690261  2.6032906  2.5335640  2.3906633  2.6816020  2.7869959
## 160  3.5929026  3.8163144  3.7211120  3.6656373  3.8934468  3.9869599
## 161  4.6450543  4.8066952  4.7027657  4.6674191  4.8069424  4.8817365
## 162  4.5521843  5.0155613  4.5045924  4.6478680  4.9217510  5.0483294
## 163  6.1723951  6.5562104  6.1596766  6.2664707  6.5138671  6.6204484
## 164  6.4635034  6.8664169  6.4468655  6.5919379  6.8248728  6.9509995
## 165  2.2346353  2.2890013  2.2542220  2.1716391  2.3474853  2.3479139
## 166  2.7741158  2.6514990  2.8396779  2.8022092  2.6512899  3.0187778
## 167  4.7834187  5.2315891  4.7555737  4.9193996  5.1735345  5.3458210
## 168  2.8558389  2.5881906  2.8213148  2.8398859  2.4889708  2.8542399
## 169  2.4276624  2.4138975  2.5288145  2.5015766  2.4817361  2.7907283
## 170  2.2710421  2.3426638  2.3811667  2.3539687  2.4354305  2.6697155
## 171  2.4859522  2.1767648  2.5754511  2.4858368  2.2957954  2.5883580
## 172  2.2601562  2.1780132  2.3729547  2.2386970  2.3118485  2.4504472
## 173  1.8521565  1.6456770  1.7539514  1.6864672  1.6780044  1.6636498
## 174  1.5058950  1.9657691  1.5367332  1.5523048  1.9702124  1.9653382
## 175  1.6450959  1.8878511  1.4786455  1.5070541  1.7097330  1.5218046
## 176  2.7182338  3.2216418  2.4041195  2.6885552  2.8508559  2.6563337
## 177  2.0767917  2.3293544  1.7202371  1.9357283  1.9934924  1.7232616
## 178  1.7383673  2.2603223  1.6528722  1.6863632  2.1447248  2.0147582
## 179  2.1384277  2.6936027  2.0488321  2.2190760  2.5788791  2.5939645
## 180  3.2090283  3.7140032  3.0251590  3.2522881  3.4963055  3.4715017
## 181  3.7164326  4.1922285  3.6532373  3.8634283  4.1279844  4.2523063
## 182  2.8272158  3.0732729  2.5559980  2.7554552  2.8194197  2.7716931
## 183  3.2317520  3.7231534  3.2172879  3.3233753  3.6849316  3.7728553
## 184  2.6091154  3.0364276  2.6238013  2.6308109  3.0358774  3.0768389
## 185  2.3662144  2.2295346  2.2471499  2.2160206  2.2246046  2.2376347
## 186  2.3991953  2.4869639  2.1329666  2.3204021  2.3038707  2.3019640
## 187  4.7390186  5.2182988  4.5370051  4.8197867  5.0017666  5.0531737
## 188  3.5933745  3.9791990  3.3497194  3.5808534  3.7192162  3.6188572
## 189  3.8014976  4.1759178  3.5287923  3.7372008  3.8708369  3.7035179
## 190  4.0343988  4.4714917  3.7911484  4.0405442  4.2232869  4.1394588
## 191  4.6505510  4.9901919  4.3165529  4.5774045  4.6773462  4.5531585
## 192  4.1819137  4.5354263  3.8895269  4.0913774  4.2645736  4.0932441
## 193  4.6835184  5.1046431  4.3951316  4.6339065  4.8251801  4.6935469
## 194  5.0183804  5.3434277  4.7136265  4.9449886  5.0367185  4.8559658
## 195  4.7824689  5.0834985  4.5048298  4.6951111  4.7976300  4.6270117
## 196  6.5328018  6.9154091  6.3045187  6.5460386  6.6903249  6.6661921
## 197  5.9711073  6.2900633  5.7653309  5.9323028  6.1064353  6.0057973
## 198  5.7549713  5.9465929  5.5387001  5.7125514  5.7701080  5.7268850
## 199  5.9204306  6.1911585  5.7026399  5.8816849  6.0148521  5.9417663
##            121        122        123        124        125        126
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
## 92                                                                   
## 93                                                                   
## 94                                                                   
## 95                                                                   
## 96                                                                   
## 97                                                                   
## 98                                                                   
## 99                                                                   
## 100                                                                  
## 101                                                                  
## 102                                                                  
## 103                                                                  
## 104                                                                  
## 105                                                                  
## 106                                                                  
## 107                                                                  
## 108                                                                  
## 109                                                                  
## 110                                                                  
## 111                                                                  
## 112                                                                  
## 113                                                                  
## 114                                                                  
## 115                                                                  
## 116                                                                  
## 117                                                                  
## 118                                                                  
## 119                                                                  
## 120                                                                  
## 121                                                                  
## 122  0.5908187                                                       
## 123  0.9962197  0.6061508                                            
## 124  1.9123389  1.6779101  1.1285711                                 
## 125  1.0994216  0.6741347  0.2499356  1.1146831                      
## 126  0.7033016  0.2450637  0.4848935  1.5988016  0.5714966           
## 127  2.2074133  2.0300978  1.5172362  0.4926439  1.4690220  1.9655875
## 128  2.2706402  2.1019826  2.0113509  2.2520183  1.9488609  2.0754870
## 129  2.3628594  2.1029401  2.0896126  2.5203438  2.0954020  2.0784646
## 130  2.3572883  2.2007918  2.0838483  2.2129791  2.0076523  2.1852861
## 131  2.3568195  2.1014397  2.1846966  2.7738877  2.1970435  2.0913957
## 132  2.2814239  2.0507502  2.1494002  2.7640013  2.1575931  2.0425966
## 133  2.3138108  2.1036263  2.2349504  2.9338935  2.2739198  2.0869122
## 134  2.1507251  1.9821682  1.9813936  2.4187798  1.9519993  1.9726809
## 135  2.6950232  2.4574057  2.3769552  2.5280446  2.3332112  2.4894841
## 136  2.3239484  2.0799137  2.0139227  2.3597750  2.0222961  2.0538225
## 137  2.1793973  1.9954345  1.9375457  2.2524000  1.9138068  1.9829397
## 138  2.3814372  2.1134048  2.1318335  2.5899759  2.1294551  2.1021062
## 139  2.5615822  2.3561441  2.1385141  2.0512121  2.0736305  2.3250541
## 140  2.3244751  2.1040980  1.9737116  2.2013756  1.9652427  2.0592665
## 141  2.6932489  2.5030441  2.2429957  2.0140556  2.2277772  2.4730603
## 142  3.8716239  3.8041154  3.3779064  2.6276762  3.3255446  3.7290654
## 143  5.8553953  5.7866851  5.6195158  5.4201020  5.5862871  5.7549801
## 144  4.2577357  4.1692152  3.9418238  3.6949381  3.9081090  4.1205212
## 145  4.6586149  4.6043716  4.3485367  3.9591828  4.2846207  4.5623124
## 146  4.9387398  4.7541732  4.5505446  4.2599990  4.5474350  4.7607367
## 147  4.5573645  4.3902582  4.3462134  4.4185039  4.3149176  4.4165077
## 148  4.5771944  4.5403131  4.2817548  3.9076948  4.2339493  4.4940289
## 149  4.3521170  4.3084428  4.0662837  3.7600972  4.0438987  4.2654652
## 150  3.9694906  3.8701165  3.7409277  3.6857840  3.7083816  3.8526500
## 151  3.7650442  3.6470438  3.6585692  3.9797685  3.6661769  3.6262493
## 152  3.8744744  3.7765495  3.7802230  4.0555211  3.7428088  3.7615442
## 153  5.5972693  5.5728754  5.6098818  5.7970023  5.5640245  5.5840503
## 154  4.0288981  3.8929349  3.8625158  4.0400874  3.8473349  3.8953910
## 155  5.5116715  5.4066087  5.4067075  5.5655001  5.3994458  5.4124222
## 156  6.3552365  6.2464139  6.2740294  6.3827169  6.2773184  6.2985115
## 157  5.1345427  4.9960982  4.9750780  5.0119112  4.9326889  5.0466709
## 158  4.0512069  3.9784620  4.1639828  4.9424920  4.2830134  3.9323934
## 159  3.0765729  2.9252556  3.1093994  3.8086899  3.1151161  2.9170412
## 160  4.0049865  3.8578755  3.9922490  4.5417248  4.0113829  3.8542790
## 161  5.0364481  4.9690516  5.1111122  5.6185400  5.1357809  4.9716262
## 162  5.0046286  4.9776487  5.1867244  5.9846140  5.3336348  4.9342569
## 163  6.5688772  6.5181571  6.6690414  7.3090823  6.7876261  6.4786921
## 164  6.8808999  6.8215726  6.9659391  7.5732777  7.0968955  6.7892416
## 165  2.7469022  2.6717246  2.7717725  3.3142050  2.7796365  2.6610487
## 166  3.2838165  3.1389478  3.2671245  3.8052101  3.3016939  3.1683895
## 167  5.2712276  5.2035542  5.3740079  6.1107456  5.5284202  5.1568558
## 168  3.1827690  3.1229863  3.2437465  3.6862016  3.2815475  3.1768364
## 169  3.0541970  2.8766904  2.9785164  3.5162425  3.0155671  2.8864345
## 170  2.9623750  2.7832166  2.8908758  3.4333481  2.9243498  2.7944783
## 171  2.9807233  2.8069600  2.8285736  3.1420419  2.8086208  2.8383833
## 172  2.8538870  2.6925425  2.7642058  3.2279179  2.7435085  2.7018558
## 173  3.5814544  3.5679615  3.5873589  3.9035714  3.5926741  3.5541680
## 174  3.6936832  3.6392339  3.7998567  4.3483580  3.8385504  3.6563597
## 175  3.5556225  3.6142389  3.7979273  4.3085564  3.8233839  3.6519375
## 176  4.1461505  4.3351727  4.6555229  5.3175475  4.7526034  4.4116105
## 177  3.6865089  3.8410733  4.0734754  4.5810437  4.1303341  3.9148465
## 178  3.7667415  3.7789891  4.0148729  4.6456516  4.0603394  3.8221118
## 179  4.0111037  4.0052211  4.2211206  4.8666676  4.3089607  4.0271307
## 180  4.4295954  4.5155049  4.7720672  5.4740004  4.8930188  4.5365476
## 181  4.9664350  4.9204728  5.0792991  5.7023547  5.2137430  4.9052779
## 182  3.9446198  4.0761538  4.2576993  4.8518909  4.3592899  4.0760969
## 183  4.6101290  4.5513012  4.7327612  5.4239970  4.8373612  4.5310213
## 184  4.1393655  4.0732243  4.2433820  4.9085345  4.3110304  4.0568098
## 185  3.6675431  3.6625198  3.6926968  4.0592022  3.7167547  3.6441648
## 186  3.6819142  3.7559975  3.8743424  4.3358554  3.9565049  3.7695559
## 187  5.6534610  5.7404763  5.9694070  6.6629525  6.1352957  5.7427317
## 188  5.1239460  5.2511669  5.4904164  6.0508650  5.5878310  5.3040437
## 189  5.2451725  5.4115295  5.6952901  6.2783355  5.7829437  5.4908799
## 190  5.4884339  5.6075879  5.8603723  6.4544541  5.9748923  5.6634569
## 191  5.8604574  6.0422620  6.3152642  6.9000105  6.4376623  6.1214616
## 192  5.5512183  5.7032724  5.9787820  6.5527063  6.0743433  5.7905838
## 193  5.9642878  6.1189398  6.4085595  7.0339769  6.5277983  6.1975394
## 194  5.9440581  6.1480175  6.4363457  6.9854667  6.5398630  6.2433817
## 195  5.7712721  5.9521362  6.2393081  6.7920496  6.3291244  6.0492921
## 196  7.5103219  7.6303876  7.8565512  8.4453194  7.9983994  7.6642622
## 197  7.1553747  7.2557396  7.4834071  7.9906218  7.5791282  7.3251226
## 198  6.9305451  7.0189407  7.2043380  7.6166435  7.2952705  7.0918347
## 199  7.0874982  7.1821075  7.3805462  7.8496223  7.4811616  7.2435136
##            127        128        129        130        131        132
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
## 92                                                                   
## 93                                                                   
## 94                                                                   
## 95                                                                   
## 96                                                                   
## 97                                                                   
## 98                                                                   
## 99                                                                   
## 100                                                                  
## 101                                                                  
## 102                                                                  
## 103                                                                  
## 104                                                                  
## 105                                                                  
## 106                                                                  
## 107                                                                  
## 108                                                                  
## 109                                                                  
## 110                                                                  
## 111                                                                  
## 112                                                                  
## 113                                                                  
## 114                                                                  
## 115                                                                  
## 116                                                                  
## 117                                                                  
## 118                                                                  
## 119                                                                  
## 120                                                                  
## 121                                                                  
## 122                                                                  
## 123                                                                  
## 124                                                                  
## 125                                                                  
## 126                                                                  
## 127                                                                  
## 128  2.3976765                                                       
## 129  2.8246786  1.1035995                                            
## 130  2.3204224  0.3055492  1.2811121                                 
## 131  3.1010835  1.3195909  0.4389692  1.5252155                      
## 132  3.0789467  1.2229742  0.5512018  1.4319177  0.2382482           
## 133  3.2687060  1.5098026  0.8583714  1.7514414  0.5009277  0.4324416
## 134  2.6345103  0.5376998  0.9358684  0.7415329  0.9954258  0.8460428
## 135  2.6093694  1.4507339  1.8137141  1.5087865  1.9236694  1.8725539
## 136  2.6469320  0.9540198  0.2982588  1.1028542  0.6473141  0.6870996
## 137  2.4558768  0.4271407  0.7847936  0.6249113  1.0079885  0.9344477
## 138  2.8940280  1.1506239  0.1570906  1.3215040  0.3828009  0.5144619
## 139  2.1527570  0.7055006  1.2752124  0.5740604  1.6376061  1.6190879
## 140  2.4392706  0.7059998  0.5919787  0.8465033  0.9671360  0.9704069
## 141  2.1410347  1.2226151  1.3724972  1.1382189  1.7896269  1.8259286
## 142  2.3642063  2.6170848  3.3677979  2.4386046  3.7313878  3.6832347
## 143  5.3788859  5.6130440  5.8614064  5.5650846  6.0090529  5.9861810
## 144  3.6587373  3.9694560  4.2764258  3.9155146  4.4625544  4.4299609
## 145  3.8073358  4.2692078  4.7780331  4.1705040  4.9949987  4.9457544
## 146  4.2171302  4.7184872  4.8218838  4.7044229  4.9906413  5.0144975
## 147  4.4207145  4.4482562  4.6275373  4.4859620  4.6732022  4.6522502
## 148  3.7673734  4.2447165  4.7402934  4.1594262  4.9515261  4.9004729
## 149  3.6652001  4.1149104  4.5209436  4.0621884  4.7127515  4.6696431
## 150  3.6986526  3.7949387  4.0365559  3.7774073  4.1634227  4.1324462
## 151  4.1584927  3.8336733  3.7684206  3.9093329  3.7686824  3.7533253
## 152  4.1362259  3.8322934  4.0469068  3.8872531  4.0510800  3.9932967
## 153  5.8110162  5.5734289  5.8404252  5.5875655  5.8466804  5.7883123
## 154  4.1081091  3.9975118  4.1286225  4.0526889  4.1577026  4.1272154
## 155  5.6624263  5.5070185  5.4901273  5.5420651  5.5082823  5.5046610
## 156  6.4130227  6.4200187  6.4322168  6.4605903  6.4419280  6.4418583
## 157  4.9510605  5.0338697  5.3135596  5.0552687  5.3523612  5.3174077
## 158  5.3037990  4.8010840  4.3120350  5.0136713  4.1065297  4.1072705
## 159  4.0670919  3.5704163  3.4293303  3.7170632  3.2895990  3.2498476
## 160  4.7978904  4.2056991  3.9333142  4.3307040  3.8236630  3.8226962
## 161  5.8216880  5.4556746  5.3023866  5.5703318  5.1930244  5.1721417
## 162  6.3721230  5.8338905  5.2350203  6.0595426  5.0049394  5.0189840
## 163  7.6534433  7.2008610  6.6505622  7.3887205  6.4695933  6.4937380
## 164  7.9349580  7.5245370  6.8856989  7.7076803  6.7166193  6.7629482
## 165  3.5358457  3.2452369  3.2581360  3.3314307  3.2005707  3.1377125
## 166  4.0049039  3.8028963  3.7081328  3.9310740  3.6104475  3.5762357
## 167  6.5136881  6.0439790  5.3563342  6.2635748  5.1466017  5.1856281
## 168  3.8275343  3.7665187  3.8042859  3.8657330  3.7483111  3.7022298
## 169  3.7615443  3.5459726  3.3568256  3.6706516  3.2794671  3.2657525
## 170  3.6984933  3.4526696  3.2269094  3.5643840  3.1542940  3.1447199
## 171  3.2792340  3.2777676  3.3597015  3.3310500  3.3648836  3.3317493
## 172  3.4191733  3.2052169  3.2366151  3.2772832  3.1981348  3.1497737
## 173  4.0365310  3.7274794  3.8784729  3.7795286  3.8732965  3.8099627
## 174  4.6053194  4.0389612  3.8144889  4.1420216  3.7120113  3.6944051
## 175  4.4921061  3.9680212  3.9803802  4.0419509  3.9015747  3.8421596
## 176  5.5715901  4.9650036  4.7277207  5.0742557  4.5759237  4.5374632
## 177  4.7691254  4.2949707  4.2677807  4.3516897  4.1829778  4.1231578
## 178  4.9030732  4.2520182  4.0558971  4.3561720  3.9077978  3.8681503
## 179  5.1760866  4.5694310  4.1763695  4.7066355  4.0218045  4.0185427
## 180  5.7925748  5.2411771  4.8309086  5.3973374  4.6543557  4.6434924
## 181  6.0721806  5.6110751  4.9898522  5.7807812  4.8317019  4.8739133
## 182  5.0934385  4.6779314  4.5364994  4.8107296  4.4202357  4.3687328
## 183  5.7727589  5.2037067  4.7056788  5.3801108  4.5181437  4.5286127
## 184  5.2135301  4.6371029  4.3126858  4.7905345  4.1426701  4.1232464
## 185  4.2146328  3.9744428  4.0806638  4.0438338  4.0472029  3.9812798
## 186  4.5549631  4.2760794  4.1777996  4.3655150  4.1114078  4.0675846
## 187  7.0250991  6.5300195  5.9508750  6.7122554  5.7589625  5.7751839
## 188  6.3010570  5.7908611  5.5178011  5.8912072  5.3843003  5.3607192
## 189  6.5076708  5.9607668  5.7577237  6.0459711  5.6072987  5.5654351
## 190  6.7391604  6.2080692  5.8340675  6.3177714  5.6751998  5.6624857
## 191  7.1614073  6.6699473  6.3795269  6.7613745  6.2077331  6.1698505
## 192  6.8009944  6.2717930  6.0288955  6.3449834  5.8609683  5.8179025
## 193  7.3188713  6.7613145  6.4083004  6.8607275  6.2174422  6.1882096
## 194  7.2169624  6.8994971  6.6766584  6.9643694  6.5297386  6.4899965
## 195  7.0132518  6.6825851  6.4971660  6.7453551  6.3458854  6.3002249
## 196  8.7502102  8.4404600  7.9938257  8.5701601  7.8201893  7.8174560
## 197  8.2435519  8.0073174  7.6998747  8.0777209  7.5480622  7.5285548
## 198  7.8355703  7.7312970  7.4806962  7.7834773  7.3638875  7.3451811
## 199  8.0979750  7.9223068  7.6205289  7.9909640  7.4831108  7.4654096
##            133        134        135        136        137        138
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
## 92                                                                   
## 93                                                                   
## 94                                                                   
## 95                                                                   
## 96                                                                   
## 97                                                                   
## 98                                                                   
## 99                                                                   
## 100                                                                  
## 101                                                                  
## 102                                                                  
## 103                                                                  
## 104                                                                  
## 105                                                                  
## 106                                                                  
## 107                                                                  
## 108                                                                  
## 109                                                                  
## 110                                                                  
## 111                                                                  
## 112                                                                  
## 113                                                                  
## 114                                                                  
## 115                                                                  
## 116                                                                  
## 117                                                                  
## 118                                                                  
## 119                                                                  
## 120                                                                  
## 121                                                                  
## 122                                                                  
## 123                                                                  
## 124                                                                  
## 125                                                                  
## 126                                                                  
## 127                                                                  
## 128                                                                  
## 129                                                                  
## 130                                                                  
## 131                                                                  
## 132                                                                  
## 133                                                                  
## 134  1.0849535                                                       
## 135  1.9956162  1.4581945                                            
## 136  0.9877616  0.8069578  1.6898528                                 
## 137  1.2090887  0.4292549  1.3340522  0.6199676                      
## 138  0.8497642  0.9666634  1.8126184  0.4082501  0.8367711           
## 139  1.9478459  1.1144320  1.5855761  1.0743265  0.8168885  1.3375176
## 140  1.2601073  0.7845964  1.6317950  0.3981698  0.4743219  0.7032961
## 141  2.1241822  1.5115093  1.8286333  1.1648188  1.1486179  1.4541666
## 142  3.9283915  3.0261448  3.0344037  3.1245854  2.8329046  3.4677096
## 143  6.1155915  5.7494361  5.8123607  5.7793889  5.6783574  5.8944534
## 144  4.5819374  4.1345888  4.2440966  4.1666255  4.0438745  4.3246318
## 145  5.1332732  4.5077600  4.5405322  4.6399227  4.4188889  4.8276184
## 146  5.0961626  4.8253653  4.1707701  4.7318298  4.6386239  4.8433513
## 147  4.6801262  4.4719829  3.8721049  4.5855386  4.3987079  4.6209187
## 148  5.0659210  4.4645342  4.5023594  4.5976495  4.3793928  4.7962887
## 149  4.7958803  4.2883148  4.2528881  4.3868571  4.1945410  4.5773679
## 150  4.2513018  3.8967488  3.9083010  3.9604064  3.8246659  4.0619741
## 151  3.7685469  3.7762836  4.0235184  3.7740646  3.7704797  3.7779558
## 152  4.0279143  3.8263889  3.9199713  4.0233957  3.8588200  4.0536809
## 153  5.8440700  5.5969951  5.6494455  5.8165718  5.6303088  5.8363554
## 154  4.1449634  3.9899775  3.7526420  4.0947624  3.9538126  4.1340121
## 155  5.5386631  5.4884381  5.4882409  5.4853256  5.4578709  5.4873181
## 156  6.4339247  6.3914243  5.8132206  6.4172695  6.3111242  6.4136434
## 157  5.3447283  5.0676410  4.2517922  5.2594868  5.0001482  5.2983146
## 158  3.8438884  4.5013989  4.9301689  4.4110389  4.5848710  4.3245548
## 159  3.1714109  3.3898878  3.7010274  3.4962781  3.4785933  3.4123639
## 160  3.7654865  4.0420816  4.3386031  4.0068006  4.0823845  3.9152518
## 161  5.0907764  5.3062664  5.5027515  5.3550995  5.3614037  5.2907574
## 162  4.7118198  5.4987339  5.9698380  5.3496482  5.5822695  5.2494877
## 163  6.2586698  6.9215757  7.3332557  6.7498833  6.9826352  6.6614380
## 164  6.5334866  7.2421996  7.6389378  6.9899194  7.2746908  6.8950145
## 165  3.1392244  3.1186133  3.5543620  3.2548752  3.1989170  3.2644021
## 166  3.4764964  3.6288315  3.4272557  3.7236518  3.6510984  3.6956497
## 167  4.8886021  5.7138674  6.1473253  5.4722343  5.7659100  5.3724419
## 168  3.6327592  3.6327771  3.3437718  3.7842370  3.6336349  3.7979737
## 169  3.1969272  3.3833538  3.4036511  3.3846043  3.3905715  3.3489810
## 170  3.1058418  3.2898038  3.4456380  3.2582156  3.3007387  3.2165409
## 171  3.3710104  3.2186422  3.0923516  3.3272298  3.2067684  3.3518951
## 172  3.1790274  3.1071195  3.2910738  3.2305216  3.1521886  3.2286259
## 173  3.8275076  3.6633595  4.0165890  3.8351847  3.7253372  3.9000497
## 174  3.6508850  3.8562182  4.2823397  3.8571382  3.9154832  3.8035096
## 175  3.8280170  3.8280648  4.2316445  3.9859045  3.9052376  3.9738165
## 176  4.4286986  4.7216740  5.1757887  4.7748239  4.7911510  4.7116755
## 177  4.1016644  4.1213280  4.5264661  4.2594617  4.1921365  4.2588974
## 178  3.8008392  4.0227186  4.4786166  4.0986560  4.1253485  4.0359717
## 179  3.8899046  4.3123947  4.7696381  4.2431828  4.3760529  4.1674253
## 180  4.4583186  4.9590541  5.4511037  4.9026350  5.0314256  4.8308734
## 181  4.6704597  5.3233519  5.7775249  5.0783408  5.3527771  4.9985241
## 182  4.2234951  4.4659401  4.9339998  4.5519697  4.5489327  4.5587486
## 183  4.3247551  4.9135176  5.3878902  4.7946096  4.9939263  4.7084118
## 184  3.9725758  4.3809083  4.8533544  4.3772807  4.4880441  4.3121996
## 185  3.9565491  3.8665935  4.2176373  4.0389024  3.9501085  4.1055313
## 186  3.9930785  4.0976645  4.4852637  4.1592057  4.1556041  4.1975886
## 187  5.5167852  6.2030877  6.6822838  6.0323102  6.2596965  5.9643261
## 188  5.2494488  5.5538731  5.9596536  5.5517170  5.6168250  5.5108404
## 189  5.4658216  5.7121444  6.0897614  5.7832196  5.7996992  5.7401774
## 190  5.5232898  5.9279621  6.3543518  5.8766220  5.9987322  5.8249461
## 191  6.0233474  6.3597950  6.7413015  6.3894121  6.4636044  6.3707648
## 192  5.7124843  5.9776548  6.3698114  6.0376009  6.0924319  6.0101562
## 193  6.0370173  6.4354971  6.8544917  6.4369017  6.5452982  6.3925131
## 194  6.3942416  6.6345445  7.0099819  6.6850417  6.7239897  6.6600078
## 195  6.2111331  6.4204579  6.7563340  6.5037152  6.5202550  6.4764282
## 196  7.6205383  8.1330087  8.5331064  8.0389255  8.2094201  7.9968172
## 197  7.4232822  7.7321669  8.0778647  7.7158720  7.8254884  7.6841472
## 198  7.2622254  7.4863162  7.7170785  7.4730537  7.5555562  7.4691115
## 199  7.3590133  7.6543501  7.9835013  7.6261656  7.7395140  7.6118421
##            139        140        141        142        143        144
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
## 92                                                                   
## 93                                                                   
## 94                                                                   
## 95                                                                   
## 96                                                                   
## 97                                                                   
## 98                                                                   
## 99                                                                   
## 100                                                                  
## 101                                                                  
## 102                                                                  
## 103                                                                  
## 104                                                                  
## 105                                                                  
## 106                                                                  
## 107                                                                  
## 108                                                                  
## 109                                                                  
## 110                                                                  
## 111                                                                  
## 112                                                                  
## 113                                                                  
## 114                                                                  
## 115                                                                  
## 116                                                                  
## 117                                                                  
## 118                                                                  
## 119                                                                  
## 120                                                                  
## 121                                                                  
## 122                                                                  
## 123                                                                  
## 124                                                                  
## 125                                                                  
## 126                                                                  
## 127                                                                  
## 128                                                                  
## 129                                                                  
## 130                                                                  
## 131                                                                  
## 132                                                                  
## 133                                                                  
## 134                                                                  
## 135                                                                  
## 136                                                                  
## 137                                                                  
## 138                                                                  
## 139                                                                  
## 140  0.7609270                                                       
## 141  0.6299581  0.9182451                                            
## 142  2.2003132  2.7846859  2.2037091                                 
## 143  5.5134637  5.6652952  5.5477154  5.5414731                      
## 144  3.8504703  4.0200564  3.8898707  3.9350935  3.9471071           
## 145  4.1175183  4.4380992  4.2073735  3.7910877  4.0208548  1.0047023
## 146  4.5324462  4.6594553  4.4343203  4.8076743  4.7566565  2.6500640
## 147  4.5093328  4.5456890  4.6163114  5.1865781  4.8920849  2.8625050
## 148  4.1110766  4.3992109  4.1857439  3.7741466  4.0206826  0.9295454
## 149  4.0090097  4.2163647  4.0480012  3.8592346  4.0164371  0.7576398
## 150  3.7696253  3.8619287  3.8482036  4.2428645  4.0595751  0.9071598
## 151  3.9695452  3.7879917  4.0559454  4.9960556  4.5423096  2.1031778
## 152  4.0260794  3.9756748  4.2366026  4.8448697  4.4697499  2.0121942
## 153  5.7277417  5.7610680  5.9256617  6.2861175  2.2804423  4.5373893
## 154  4.1096088  4.0634533  4.2269834  4.8972479  4.5528789  2.1802395
## 155  5.5607955  5.4918340  5.6131151  6.3112443  2.1694981  4.4437602
## 156  6.4643311  6.4327606  6.4805482  7.1495400  3.9742850  5.5548238
## 157  5.1067176  5.2084311  5.2411065  5.6476960  5.4101395  3.7056411
## 158  5.1455231  4.5750554  5.1813471  6.5488710  6.6887526  5.2089723
## 159  3.9079161  3.5774908  4.1063845  5.3090206  5.6156641  3.8828020
## 160  4.4377286  4.1100491  4.5424072  5.7994420  5.1735404  3.2021981
## 161  5.7048126  5.4289198  5.8188531  6.8226530  4.2898916  5.7220143
## 162  6.1805552  5.5441356  6.1626715  7.5976396  7.6206805  6.3102069
## 163  7.4660346  6.9219434  7.4296375  8.7277550  6.7141063  7.5983304
## 164  7.7414975  7.1817518  7.6452097  9.0351845  7.0771645  7.9129262
## 165  3.5107099  3.2859374  3.6870127  4.6808642  5.2055273  3.2882900
## 166  4.0655850  3.7991166  4.1843645  5.2884911  5.6782031  3.9667704
## 167  6.3290872  5.6831445  6.2538979  7.7481255  7.7630523  6.4737494
## 168  4.0033227  3.8209768  4.1094117  5.0669761  5.5696293  3.8327267
## 169  3.7654336  3.4693586  3.8523650  5.0646322  5.4735387  3.6740583
## 170  3.6532485  3.3539973  3.7318936  5.0002989  5.4050743  3.5782379
## 171  3.4191624  3.3384281  3.5560789  4.4943339  5.1094181  3.1870022
## 172  3.4214811  3.2608334  3.6022981  4.6149008  5.1448828  3.2204881
## 173  3.9288176  3.8151681  4.0854105  4.7535983  6.0191014  4.4814366
## 174  4.2744023  3.9619278  4.3602221  5.5868747  6.4705353  5.0382112
## 175  4.2420867  4.0311075  4.3842716  5.3706206  6.3657674  4.9238947
## 176  5.2754328  4.9025808  5.3044779  6.5769440  7.2641818  5.9892152
## 177  4.5519627  4.3307970  4.6314202  5.6608059  6.6086124  5.2244485
## 178  4.5512336  4.2234546  4.6655417  5.9007269  6.6987143  5.3191574
## 179  4.8358758  4.4014629  4.8557833  6.2320140  6.9523569  5.6002420
## 180  5.5484731  5.0619761  5.5434949  6.8904342  7.7579176  6.5403058
## 181  5.8228233  5.2758607  5.7274576  7.1958692  8.0045671  6.8091403
## 182  4.9937601  4.6233420  5.0516936  6.0425474  7.1969763  5.8938357
## 183  5.4924382  4.9725152  5.5033008  6.8835623  7.7305307  6.5015381
## 184  4.9460964  4.5164472  5.0381575  6.2742044  7.2663591  5.9793814
## 185  4.2037533  4.0411463  4.3507990  5.0262823  6.5210823  5.1158792
## 186  4.5035096  4.2240077  4.5424552  5.4964763  6.8163998  5.4566992
## 187  6.8125747  6.2296760  6.7131660  8.1257578  8.8067030  7.6963712
## 188  6.0420919  5.6840315  6.0357358  7.2111755  7.7865642  6.5977098
## 189  6.2413712  5.9181826  6.2698301  7.4143980  7.9567903  6.8057148
## 190  6.4581148  6.0473178  6.4191776  7.6969580  8.1836074  7.0400035
## 191  6.9427195  6.5647544  6.9156803  8.0830748  8.5728092  7.4801824
## 192  6.5390112  6.2084310  6.5520147  7.7134781  8.2285941  7.1104004
## 193  7.0406916  6.6331020  7.0165033  8.2825480  8.7021030  7.6238574
## 194  7.1466034  6.8367991  7.1324775  8.2398727  8.8480110  7.8169668
## 195  6.9409287  6.6516129  6.9584127  8.0434843  8.6691358  7.6234634
## 196  8.6875817  8.2240715  8.6053036  9.8158586 10.0213621  9.0537421
## 197  8.2154532  7.8901758  8.1882914  9.2949966  9.3495753  8.3624122
## 198  7.8939868  7.6268903  7.8507497  8.8542462  8.9984746  7.9851303
## 199  8.1118702  7.7932274  8.0692904  9.1274460  9.2268652  8.2235102
##            145        146        147        148        149        150
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
## 92                                                                   
## 93                                                                   
## 94                                                                   
## 95                                                                   
## 96                                                                   
## 97                                                                   
## 98                                                                   
## 99                                                                   
## 100                                                                  
## 101                                                                  
## 102                                                                  
## 103                                                                  
## 104                                                                  
## 105                                                                  
## 106                                                                  
## 107                                                                  
## 108                                                                  
## 109                                                                  
## 110                                                                  
## 111                                                                  
## 112                                                                  
## 113                                                                  
## 114                                                                  
## 115                                                                  
## 116                                                                  
## 117                                                                  
## 118                                                                  
## 119                                                                  
## 120                                                                  
## 121                                                                  
## 122                                                                  
## 123                                                                  
## 124                                                                  
## 125                                                                  
## 126                                                                  
## 127                                                                  
## 128                                                                  
## 129                                                                  
## 130                                                                  
## 131                                                                  
## 132                                                                  
## 133                                                                  
## 134                                                                  
## 135                                                                  
## 136                                                                  
## 137                                                                  
## 138                                                                  
## 139                                                                  
## 140                                                                  
## 141                                                                  
## 142                                                                  
## 143                                                                  
## 144                                                                  
## 145                                                                  
## 146  3.0281227                                                       
## 147  3.2562624  1.7294894                                            
## 148  0.3300703  2.9614561  3.1975650                                 
## 149  0.9098961  2.4731436  2.7203874  0.6610437                      
## 150  1.6110869  2.2967854  2.1192402  1.5472678  1.1587445           
## 151  2.9581791  3.0332704  2.4532304  2.8614218  2.4403154  1.4612094
## 152  2.5812778  3.0051865  2.0208273  2.5050664  2.1581394  1.2884282
## 153  4.6871805  5.1550253  4.5281125  4.6741373  4.5682015  4.2434123
## 154  2.7894477  2.1266080  1.1110731  2.6931483  2.1856649  1.3548345
## 155  4.8538031  4.6329339  4.3452285  4.8169592  4.5727511  4.1280117
## 156  5.8828231  4.4756990  4.1618451  5.8314100  5.4576528  5.0495955
## 157  3.8913492  2.2546613  1.0832333  3.8505683  3.4403138  3.0256117
## 158  6.0151808  5.5264541  4.8995294  5.8559450  5.3999282  4.7462343
## 159  4.5164488  4.4166268  3.5654606  4.4392924  4.0998328  3.3387122
## 160  4.0494211  3.7367174  2.9229344  3.9668703  3.5464829  2.5279447
## 161  6.2281384  6.0029730  5.3924861  6.1523007  5.8607444  5.3184461
## 162  7.1551225  6.5490299  5.9874792  6.9772535  6.4990328  5.8692720
## 163  8.3584158  7.7967203  7.3811277  8.2083541  7.7956355  7.2461816
## 164  8.7100749  7.9986705  7.7097488  8.5603024  8.1303222  7.5680004
## 165  3.8633937  4.2091431  3.5847318  3.7808566  3.5031672  2.8881674
## 166  4.5665157  3.7252631  2.9137737  4.4600692  4.0085263  3.3409081
## 167  7.3568741  6.5911496  6.1769921  7.1815574  6.6889114  6.0599900
## 168  4.3373212  3.5395605  2.7805324  4.2215211  3.7760182  3.2124292
## 169  4.3418922  3.7372460  3.1132065  4.2459482  3.8237098  3.1142761
## 170  4.2652904  3.8407217  3.2905280  4.1818361  3.7923940  3.0558087
## 171  3.6751287  3.3247002  2.7530231  3.6157140  3.2737751  2.6607586
## 172  3.7694514  3.8091802  3.1592363  3.7125782  3.4146917  2.7409667
## 173  4.8119963  5.2529538  4.8426563  4.7379110  4.5637884  4.2715481
## 174  5.5716932  5.5569524  5.0949245  5.4999544  5.2345507  4.6829787
## 175  5.3280825  5.5711011  5.0282576  5.2554005  5.0365265  4.5791777
## 176  6.5190126  6.4202066  5.8878904  6.4062961  6.0944483  5.5607777
## 177  5.6314806  5.8010451  5.3261768  5.5431821  5.3058418  4.8691051
## 178  5.8378959  5.8526302  5.2774629  5.7588244  5.4903509  4.9182419
## 179  6.2287326  5.9851083  5.5310177  6.1231881  5.7887273  5.2065914
## 180  7.1596414  6.9012683  6.4434493  7.0289821  6.6803752  6.1632660
## 181  7.5320646  7.0009908  6.7449970  7.3989251  7.0122684  6.4791013
## 182  6.3825518  6.4460333  5.9768681  6.2464331  5.9522841  5.5946875
## 183  7.1713423  6.8225219  6.3773559  7.0495688  6.6942111  6.1450867
## 184  6.5572594  6.4413129  5.9171229  6.4563525  6.1569816  5.6358860
## 185  5.4507603  5.7839876  5.3762194  5.3634990  5.1744821  4.9118546
## 186  5.9027940  5.9628425  5.6218965  5.7890052  5.5243767  5.1930612
## 187  8.4182938  7.8835009  7.5463927  8.2487982  7.8294668  7.3360835
## 188  7.1304146  6.9597117  6.5436383  7.0136465  6.7047686  6.2317411
## 189  7.2878401  7.1595791  6.6561664  7.1784785  6.8864793  6.4035222
## 190  7.6298098  7.3309211  6.9443888  7.5031235  7.1655402  6.6620390
## 191  8.0157142  7.7348246  7.3155091  7.8743129  7.5381561  7.0936696
## 192  7.6081591  7.4425730  6.9826660  7.4936769  7.1982391  6.7211548
## 193  8.1954228  7.8849395  7.4420840  8.0621956  7.7232245  7.2204012
## 194  8.2741193  8.1226834  7.7204452  8.1602872  7.8800071  7.4525482
## 195  8.0602270  7.9100947  7.4555042  7.9548488  7.6820938  7.2424488
## 196  9.6861986  9.2154095  8.8914531  9.5271912  9.1510853  8.7094554
## 197  8.8810340  8.5923737  8.2397103  8.7690553  8.4727635  8.0143963
## 198  8.4574102  8.0921137  7.8263438  8.3477172  8.0538498  7.6549209
## 199  8.7403275  8.4394939  8.1433318  8.6211665  8.3206223  7.9017682
##            151        152        153        154        155        156
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
## 92                                                                   
## 93                                                                   
## 94                                                                   
## 95                                                                   
## 96                                                                   
## 97                                                                   
## 98                                                                   
## 99                                                                   
## 100                                                                  
## 101                                                                  
## 102                                                                  
## 103                                                                  
## 104                                                                  
## 105                                                                  
## 106                                                                  
## 107                                                                  
## 108                                                                  
## 109                                                                  
## 110                                                                  
## 111                                                                  
## 112                                                                  
## 113                                                                  
## 114                                                                  
## 115                                                                  
## 116                                                                  
## 117                                                                  
## 118                                                                  
## 119                                                                  
## 120                                                                  
## 121                                                                  
## 122                                                                  
## 123                                                                  
## 124                                                                  
## 125                                                                  
## 126                                                                  
## 127                                                                  
## 128                                                                  
## 129                                                                  
## 130                                                                  
## 131                                                                  
## 132                                                                  
## 133                                                                  
## 134                                                                  
## 135                                                                  
## 136                                                                  
## 137                                                                  
## 138                                                                  
## 139                                                                  
## 140                                                                  
## 141                                                                  
## 142                                                                  
## 143                                                                  
## 144                                                                  
## 145                                                                  
## 146                                                                  
## 147                                                                  
## 148                                                                  
## 149                                                                  
## 150                                                                  
## 151                                                                  
## 152  1.1075324                                                       
## 153  4.3295951  4.0300131                                            
## 154  1.3903358  1.0404052  4.2302026                                 
## 155  4.0111305  4.0973786  1.6981557  4.0462833                      
## 156  5.0976237  5.0041871  3.2765893  4.4787292  2.6126615           
## 157  3.4775438  2.9043939  4.8851473  2.1194969  4.8670032  4.1650922
## 158  3.6154292  4.1473046  6.1321662  4.2127341  5.6116006  6.4368508
## 159  2.5651328  2.7135004  4.9813401  2.9256325  4.7998957  5.6617724
## 160  1.1178886  1.8408664  4.6349891  2.0334096  4.2048628  5.2158169
## 161  4.7734961  4.9126976  3.2998504  4.9894190  2.8896245  4.0437513
## 162  4.6626352  5.2806762  7.0503659  5.3160365  6.4260836  7.2001151
## 163  6.2509796  6.7972306  6.1440869  6.8177858  5.2746870  6.2784507
## 164  6.5608487  7.2044996  6.6552242  7.1626956  5.6287015  6.5604087
## 165  2.4080976  2.5372066  4.8336511  2.8472091  4.7262183  5.7721749
## 166  2.8340419  2.8751148  5.0835703  2.6180637  4.7929406  5.0335518
## 167  4.8634563  5.5740355  7.3383137  5.5334113  6.5627301  7.3108037
## 168  2.9358172  2.8670334  4.9999186  2.5642308  4.8091511  4.9374898
## 169  2.5168653  2.7551786  5.0513913  2.6249558  4.6705395  5.2389630
## 170  2.4319698  2.7581513  5.0479543  2.7197212  4.6498228  5.3852340
## 171  2.5555237  2.5077067  4.7908942  2.3865770  4.5953672  5.1319488
## 172  2.3985417  2.4348786  4.7681174  2.5753432  4.6182886  5.4538493
## 173  4.1312644  4.1267968  5.7935863  4.3365981  5.7897658  6.6830458
## 174  4.1576195  4.4231895  6.0910049  4.5620848  5.8275219  6.6927706
## 175  4.2341989  4.3185636  5.8958205  4.5188612  5.8656597  6.6792965
## 176  4.9402497  5.2462867  6.6437462  5.3588431  6.4489842  7.1141666
## 177  4.5242219  4.6751626  6.1357480  4.8261354  6.0716868  6.8083950
## 178  4.3425516  4.5695462  6.1565012  4.7414663  5.9730516  6.7962678
## 179  4.4797393  4.8878175  6.5100751  4.9706817  6.1142713  6.9147429
## 180  5.4006694  5.8100428  7.2531299  5.8900965  6.8814615  7.6013762
## 181  5.6304284  6.2122155  7.7346062  6.1961505  7.0790463  7.8312682
## 182  5.0658091  5.2809389  6.7548552  5.4255489  6.6043041  7.3642935
## 183  5.3124772  5.7526211  7.3013241  5.8235814  6.8243835  7.6151344
## 184  4.9466174  5.2346659  6.8021381  5.3766386  6.5010558  7.3370122
## 185  4.7119728  4.7260643  6.2660045  4.9035533  6.2404097  7.0644097
## 186  4.8280164  5.0273368  6.5363229  5.1229016  6.3461166  7.0966124
## 187  6.4193725  6.9881556  8.3764457  6.9809030  7.7888543  8.4281915
## 188  5.6338758  5.9732611  7.2960262  6.0446381  7.0116629  7.6608425
## 189  5.8476530  6.1088954  7.3366636  6.1956262  7.1591068  7.7261825
## 190  5.9671842  6.3917597  7.6947104  6.4337810  7.3050138  7.9396343
## 191  6.4636271  6.8137824  8.0046885  6.8435062  7.7049883  8.2140970
## 192  6.1469524  6.4450684  7.6450474  6.5178180  7.4083775  7.9862387
## 193  6.5161203  6.9089640  8.1067515  6.9526259  7.7615729  8.3171886
## 194  6.9390903  7.2309555  8.2906631  7.2882865  8.0802552  8.5849855
## 195  6.7536064  6.9914641  8.0660391  7.0515890  7.8988315  8.3738812
## 196  7.9211255  8.4046869  9.5548923  8.3990124  9.0588994  9.5805807
## 197  7.4165292  7.7781798  8.8670705  7.8088342  8.5124349  9.0506067
## 198  7.1897638  7.5059532  8.6123384  7.4682509  8.2542774  8.6731260
## 199  7.3336728  7.7017130  8.8202841  7.7131368  8.4398960  8.9787188
##            157        158        159        160        161        162
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
## 92                                                                   
## 93                                                                   
## 94                                                                   
## 95                                                                   
## 96                                                                   
## 97                                                                   
## 98                                                                   
## 99                                                                   
## 100                                                                  
## 101                                                                  
## 102                                                                  
## 103                                                                  
## 104                                                                  
## 105                                                                  
## 106                                                                  
## 107                                                                  
## 108                                                                  
## 109                                                                  
## 110                                                                  
## 111                                                                  
## 112                                                                  
## 113                                                                  
## 114                                                                  
## 115                                                                  
## 116                                                                  
## 117                                                                  
## 118                                                                  
## 119                                                                  
## 120                                                                  
## 121                                                                  
## 122                                                                  
## 123                                                                  
## 124                                                                  
## 125                                                                  
## 126                                                                  
## 127                                                                  
## 128                                                                  
## 129                                                                  
## 130                                                                  
## 131                                                                  
## 132                                                                  
## 133                                                                  
## 134                                                                  
## 135                                                                  
## 136                                                                  
## 137                                                                  
## 138                                                                  
## 139                                                                  
## 140                                                                  
## 141                                                                  
## 142                                                                  
## 143                                                                  
## 144                                                                  
## 145                                                                  
## 146                                                                  
## 147                                                                  
## 148                                                                  
## 149                                                                  
## 150                                                                  
## 151                                                                  
## 152                                                                  
## 153                                                                  
## 154                                                                  
## 155                                                                  
## 156                                                                  
## 157                                                                  
## 158  5.6606128                                                       
## 159  4.2874758  2.2503051                                            
## 160  3.8747991  3.1056912  2.3899346                                 
## 161  5.8949085  4.3600367  3.9710107  4.6136776                      
## 162  6.7255719  1.3158053  3.5371347  4.0491513  5.0304661           
## 163  8.0446037  4.2572471  5.4764287  5.7676995  3.4277953  3.9748744
## 164  8.3923854  4.5487431  5.8758958  6.0597822  3.9775956  4.1454124
## 165  4.3387278  2.7763011  1.0261065  2.6085219  4.1540703  4.0321789
## 166  3.4566072  2.6524209  1.3936414  2.7855290  4.1494086  3.8459878
## 167  6.9414268  1.7030561  3.8802884  4.2528382  5.2608781  0.7166151
## 168  3.2225628  3.1215206  1.8104163  3.0683368  4.3097494  4.2788272
## 169  3.8198237  2.4077725  1.0027178  2.4925999  4.0628303  3.6573407
## 170  4.0458238  2.4377271  0.9572504  2.4181694  4.0691777  3.6825443
## 171  3.3744298  3.4127937  1.5763626  2.8683877  4.3351727  4.6775108
## 172  3.8683958  3.0502432  1.0585617  2.6158959  4.1813092  4.3356604
## 173  5.3932820  4.1304408  3.0637050  4.3935244  5.0816569  5.1421161
## 174  5.7122590  3.4816502  2.8431659  4.0878062  4.8543958  4.3390961
## 175  5.5517536  3.9116887  2.9895910  4.3041118  4.9621877  4.8228008
## 176  6.3942800  3.8283439  3.7456058  4.7653578  5.2849473  4.3136176
## 177  5.8115193  4.1359217  3.4218113  4.5825896  5.1803323  4.9237200
## 178  5.8442568  3.5298597  2.9614304  4.2074609  4.8939522  4.3206953
## 179  6.1627053  3.1061915  3.1530251  4.2435657  4.9407726  3.6982156
## 180  7.0247453  3.6585181  4.1578164  5.1224181  5.5548179  3.8932569
## 181  7.4175529  3.6099921  4.5183813  5.2844806  5.8126608  3.6384280
## 182  6.5158044  3.8470465  3.8696874  5.0240590  5.4282782  4.3812158
## 183  7.0185192  3.3835971  4.0043959  4.9703462  5.4812749  3.6388562
## 184  6.5219763  3.5357581  3.5698758  4.7233930  5.2575088  4.1053595
## 185  5.8850693  4.3986361  3.6282885  4.9003506  5.4163385  5.2839961
## 186  6.1545362  4.0967674  3.7471981  4.9008657  5.3998390  4.7998567
## 187  8.1582609  4.0411828  5.3373011  6.0201219  6.3616391  3.6657759
## 188  7.0478460  4.1866116  4.3216743  5.4611787  5.6950017  4.5465548
## 189  7.0842360  4.5673746  4.5355536  5.6725331  5.8549904  4.9512698
## 190  7.4667561  4.2581268  4.6941324  5.7064974  5.9341244  4.4232202
## 191  7.7459844  4.8710725  5.2761670  6.2361267  6.3731612  4.9893612
## 192  7.4105900  4.8325550  4.9086054  5.9463267  6.1358432  5.1384166
## 193  7.9016542  4.8094037  5.2882011  6.2165780  6.3771258  4.8697108
## 194  8.1040242  5.6550540  5.7693527  6.7719835  6.8114408  5.8704864
## 195  7.8136322  5.5448933  5.5228351  6.5914701  6.6308688  5.8474941
## 196  9.3894793  5.8545605  6.8536675  7.5700672  7.6437200  5.5364345
## 197  8.6661893  5.9852286  6.3023870  7.1675829  7.2620099  6.0841845
## 198  8.2054262  6.0089280  6.1415070  7.0399598  7.1497872  6.2433148
## 199  8.5793615  5.9136417  6.2548396  7.1237228  7.2263842  6.0244612
##            163        164        165        166        167        168
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
## 21                                                                   
## 22                                                                   
## 23                                                                   
## 24                                                                   
## 25                                                                   
## 26                                                                   
## 27                                                                   
## 28                                                                   
## 29                                                                   
## 30                                                                   
## 31                                                                   
## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
## 92                                                                   
## 93                                                                   
## 94                                                                   
## 95                                                                   
## 96                                                                   
## 97                                                                   
## 98                                                                   
## 99                                                                   
## 100                                                                  
## 101                                                                  
## 102                                                                  
## 103                                                                  
## 104                                                                  
## 105                                                                  
## 106                                                                  
## 107                                                                  
## 108                                                                  
## 109                                                                  
## 110                                                                  
## 111                                                                  
## 112                                                                  
## 113                                                                  
## 114                                                                  
## 115                                                                  
## 116                                                                  
## 117                                                                  
## 118                                                                  
## 119                                                                  
## 120                                                                  
## 121                                                                  
## 122                                                                  
## 123                                                                  
## 124                                                                  
## 125                                                                  
## 126                                                                  
## 127                                                                  
## 128                                                                  
## 129                                                                  
## 130                                                                  
## 131                                                                  
## 132                                                                  
## 133                                                                  
## 134                                                                  
## 135                                                                  
## 136                                                                  
## 137                                                                  
## 138                                                                  
## 139                                                                  
## 140                                                                  
## 141                                                                  
## 142                                                                  
## 143                                                                  
## 144                                                                  
## 145                                                                  
## 146                                                                  
## 147                                                                  
## 148                                                                  
## 149                                                                  
## 150                                                                  
## 151                                                                  
## 152                                                                  
## 153                                                                  
## 154                                                                  
## 155                                                                  
## 156                                                                  
## 157                                                                  
## 158                                                                  
## 159                                                                  
## 160                                                                  
## 161                                                                  
## 162                                                                  
## 163                                                                  
## 164  0.8553749                                                       
## 165  5.8259335  6.2109746                                            
## 166  5.7196702  6.0712195  1.7733789                                 
## 167  3.9560748  3.9954347  4.3480884  4.1143214                      
## 168  6.0669836  6.4167587  1.8945882  0.7113454  4.5659709           
## 169  5.5461555  5.8636378  1.2874534  0.7481646  3.8816415  1.1764077
## 170  5.5432953  5.8427355  1.0682326  1.1370645  3.8900268  1.4804466
## 171  6.3124633  6.6537738  1.3335730  1.2564068  4.9116135  1.1802861
## 172  6.0426682  6.4121620  0.6788765  1.4271094  4.6082697  1.5561038
## 173  6.6730766  7.0419513  2.7195659  3.3386285  5.4247745  3.2989573
## 174  5.9978658  6.2716190  2.8107856  3.2154214  4.5611268  3.3481163
## 175  6.4344479  6.7712712  2.7933798  3.2957640  5.1368666  3.2553463
## 176  6.0473814  6.2649784  3.7121239  3.9399268  4.6164719  3.8978703
## 177  6.5232618  6.8059712  3.1525623  3.5995064  5.2260987  3.4652102
## 178  6.0118509  6.3034489  2.9457119  3.3232109  4.6000932  3.4184798
## 179  5.5194741  5.7260564  3.2515215  3.4584878  3.8914702  3.6385182
## 180  5.6646481  5.8368299  4.2802891  4.3943350  4.0967790  4.5321732
## 181  5.3569793  5.3843927  4.7182279  4.7301198  3.5961240  5.0029505
## 182  6.0900950  6.3892190  3.8077060  4.0827959  4.6825799  4.1057477
## 183  5.4161148  5.5940924  4.2491330  4.3128969  3.7566211  4.6052693
## 184  5.7976673  6.0769482  3.7248157  3.9331965  4.3203853  4.1744571
## 185  6.7793331  7.1395894  3.3824238  3.8380945  5.5558835  3.8282933
## 186  6.3863015  6.6577168  3.5492072  3.8783658  5.0342090  3.8560068
## 187  5.4210294  5.4176790  5.5396618  5.4741304  3.6932853  5.6729161
## 188  6.1761278  6.3445685  4.2886018  4.4698300  4.7668487  4.4788314
## 189  6.5215178  6.7160061  4.4798028  4.6393483  5.2207645  4.5859052
## 190  6.0450283  6.1417513  4.7075076  4.8230921  4.5831407  4.8776306
## 191  6.5195716  6.6290170  5.2112981  5.2740782  5.1886643  5.2375540
## 192  6.6384473  6.7916703  4.8108123  4.9757321  5.3600173  4.9390436
## 193  6.3966917  6.4813452  5.2806661  5.3526597  5.0458551  5.3726573
## 194  7.2411391  7.3566049  5.6525156  5.8034174  6.0788932  5.7145003
## 195  7.2327459  7.3878771  5.4226656  5.5448740  6.0779440  5.4594739
## 196  6.8467456  6.8155980  6.9511041  6.9083035  5.5771513  7.0149433
## 197  7.3402293  7.3952922  6.2625956  6.3560520  6.1927615  6.3836159
## 198  7.4928976  7.5590573  6.0412955  6.0624812  6.3400500  6.0333595
## 199  7.2864292  7.3374655  6.1867214  6.2763044  6.1148226  6.2982696
##            169        170        171        172        173        174
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
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## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
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## 59                                                                   
## 60                                                                   
## 61                                                                   
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## 65                                                                   
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## 67                                                                   
## 68                                                                   
## 69                                                                   
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## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
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## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
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## 89                                                                   
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## 99                                                                   
## 100                                                                  
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## 120                                                                  
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## 123                                                                  
## 124                                                                  
## 125                                                                  
## 126                                                                  
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## 133                                                                  
## 134                                                                  
## 135                                                                  
## 136                                                                  
## 137                                                                  
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## 140                                                                  
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## 142                                                                  
## 143                                                                  
## 144                                                                  
## 145                                                                  
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## 149                                                                  
## 150                                                                  
## 151                                                                  
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## 153                                                                  
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## 156                                                                  
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## 159                                                                  
## 160                                                                  
## 161                                                                  
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## 163                                                                  
## 164                                                                  
## 165                                                                  
## 166                                                                  
## 167                                                                  
## 168                                                                  
## 169                                                                  
## 170  0.4231360                                                       
## 171  1.0708497  1.1110381                                            
## 172  1.0008346  0.8553178  0.7398233                                 
## 173  3.1217810  3.0472716  2.9871681  2.8189868                      
## 174  2.9239623  2.8053825  3.1673151  2.9218810  1.4481559           
## 175  3.1083549  3.0179555  3.1374016  2.9314277  1.0811397  0.9736324
## 176  3.8042029  3.7243922  4.1569016  3.9519192  2.8375178  2.0100248
## 177  3.4417822  3.3382376  3.4841186  3.3267381  1.7831714  1.4990777
## 178  3.1061725  2.9979887  3.3644119  3.1002804  1.7128793  0.6533768
## 179  3.1970529  3.1025782  3.6946524  3.4383489  2.3170563  1.0458995
## 180  4.2198873  4.1680413  4.7708641  4.5268672  3.1892402  2.1930204
## 181  4.4654908  4.4029323  5.1455388  4.9164301  3.8598190  2.7672945
## 182  3.9502752  3.9246545  4.2867245  4.0681095  2.2195197  1.8599365
## 183  4.0912374  4.0471303  4.7208038  4.4462044  3.2279779  2.1863047
## 184  3.7257183  3.6738423  4.1748324  3.8940636  2.3509503  1.4836001
## 185  3.6787539  3.6341566  3.6468369  3.4930297  1.0024582  1.6732694
## 186  3.7058226  3.6475730  3.8667710  3.7197710  1.6308846  1.4541608
## 187  5.3133135  5.2881998  6.0541049  5.8217254  4.8365960  3.8439233
## 188  4.3217473  4.2455692  4.6972901  4.5096884  3.6372843  2.9588800
## 189  4.5580528  4.4880052  4.8506898  4.6836555  3.8430357  3.2355082
## 190  4.6682156  4.5860724  5.1373551  4.9402752  4.1839223  3.3602386
## 191  5.2138211  5.1528249  5.5990907  5.4465366  4.6864892  4.0270574
## 192  4.8899915  4.8010498  5.1783139  5.0132746  4.2295222  3.6001455
## 193  5.2632395  5.1865819  5.7016799  5.5162919  4.8225516  4.0379932
## 194  5.7333171  5.6524037  5.9909847  5.8572157  4.9385242  4.3698771
## 195  5.4994639  5.4291324  5.7191812  5.5955542  4.6687262  4.1408735
## 196  6.8099137  6.7724138  7.3910100  7.2038362  6.4687331  5.6968696
## 197  6.2549093  6.1702707  6.5889252  6.4379195  5.8693537  5.2440171
## 198  5.9904258  5.9237647  6.2262728  6.1565752  5.5719656  5.0759645
## 199  6.1698988  6.0902608  6.4969010  6.3611408  5.7628650  5.1863285
##            175        176        177        178        179        180
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
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## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
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## 95                                                                   
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## 99                                                                   
## 100                                                                  
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## 119                                                                  
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## 123                                                                  
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## 125                                                                  
## 126                                                                  
## 127                                                                  
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## 130                                                                  
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## 134                                                                  
## 135                                                                  
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## 137                                                                  
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## 139                                                                  
## 140                                                                  
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## 143                                                                  
## 144                                                                  
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## 149                                                                  
## 150                                                                  
## 151                                                                  
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## 153                                                                  
## 154                                                                  
## 155                                                                  
## 156                                                                  
## 157                                                                  
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## 159                                                                  
## 160                                                                  
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## 162                                                                  
## 163                                                                  
## 164                                                                  
## 165                                                                  
## 166                                                                  
## 167                                                                  
## 168                                                                  
## 169                                                                  
## 170                                                                  
## 171                                                                  
## 172                                                                  
## 173                                                                  
## 174                                                                  
## 175                                                                  
## 176  1.8731928                                                       
## 177  0.8992104  1.3246698                                            
## 178  0.8958775  1.5679788  1.1684694                                 
## 179  1.6901244  1.5542064  1.7849324  0.9907223                      
## 180  2.5382815  1.6608762  2.4062553  1.9911180  1.3712401           
## 181  3.4690641  2.9029255  3.4887508  2.8361656  1.9385690  1.4957101
## 182  1.7979154  1.7797427  1.8311237  1.7159227  1.6342629  1.3561636
## 183  2.8540589  2.6239528  3.0424512  2.2177266  1.5012915  1.2309589
## 184  2.0525586  2.4274172  2.4287720  1.5378880  1.2977231  1.5388309
## 185  1.4408205  2.8734059  1.9879592  1.8470784  2.3327081  2.8347392
## 186  1.3780514  1.9876931  1.4611440  1.4596132  1.6338738  1.8846328
## 187  4.2951084  3.1195848  4.0824551  3.6974684  2.8624186  1.8635767
## 188  3.0136319  2.3064036  2.7007058  2.7150201  2.5592913  2.8195488
## 189  3.1291274  2.3276571  2.6963667  2.8733979  2.9020851  3.1170240
## 190  3.5388065  2.5705276  3.1679646  3.0934948  2.7707155  2.8674916
## 191  4.0302324  2.9404840  3.4933459  3.6428500  3.4654274  3.4179622
## 192  3.5682277  2.7466285  3.0717549  3.2074598  3.2106738  3.3964385
## 193  4.1321979  3.0007918  3.6328769  3.6543722  3.4239666  3.3767071
## 194  4.2669618  3.3142653  3.7177561  3.9980237  3.9744074  3.8109247
## 195  4.0150422  3.2319983  3.5194451  3.7646977  3.8267918  3.7611286
## 196  5.9464670  4.8842728  5.6091876  5.4665601  4.9845147  4.5942541
## 197  5.3571880  4.6445805  4.9876863  4.9755990  4.8353931  4.9400749
## 198  5.1434843  4.6128743  4.7796568  4.8555839  4.7761930  4.9933122
## 199  5.3103750  4.6587670  4.9546721  4.9503848  4.7873063  4.9078306
##            181        182        183        184        185        186
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
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## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
## 79                                                                   
## 80                                                                   
## 81                                                                   
## 82                                                                   
## 83                                                                   
## 84                                                                   
## 85                                                                   
## 86                                                                   
## 87                                                                   
## 88                                                                   
## 89                                                                   
## 90                                                                   
## 91                                                                   
## 92                                                                   
## 93                                                                   
## 94                                                                   
## 95                                                                   
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## 97                                                                   
## 98                                                                   
## 99                                                                   
## 100                                                                  
## 101                                                                  
## 102                                                                  
## 103                                                                  
## 104                                                                  
## 105                                                                  
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## 108                                                                  
## 109                                                                  
## 110                                                                  
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## 112                                                                  
## 113                                                                  
## 114                                                                  
## 115                                                                  
## 116                                                                  
## 117                                                                  
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## 119                                                                  
## 120                                                                  
## 121                                                                  
## 122                                                                  
## 123                                                                  
## 124                                                                  
## 125                                                                  
## 126                                                                  
## 127                                                                  
## 128                                                                  
## 129                                                                  
## 130                                                                  
## 131                                                                  
## 132                                                                  
## 133                                                                  
## 134                                                                  
## 135                                                                  
## 136                                                                  
## 137                                                                  
## 138                                                                  
## 139                                                                  
## 140                                                                  
## 141                                                                  
## 142                                                                  
## 143                                                                  
## 144                                                                  
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## 148                                                                  
## 149                                                                  
## 150                                                                  
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## 153                                                                  
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## 155                                                                  
## 156                                                                  
## 157                                                                  
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## 159                                                                  
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## 167                                                                  
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## 169                                                                  
## 170                                                                  
## 171                                                                  
## 172                                                                  
## 173                                                                  
## 174                                                                  
## 175                                                                  
## 176                                                                  
## 177                                                                  
## 178                                                                  
## 179                                                                  
## 180                                                                  
## 181                                                                  
## 182  2.4723744                                                       
## 183  1.0218782  1.9141978                                            
## 184  1.9543975  1.4893247  1.0437932                                 
## 185  3.5298998  1.7687162  2.8475953  1.9248074                      
## 186  2.7287050  0.9771952  2.2319231  1.5793629  1.1500829           
## 187  1.6093785  2.9468033  2.1438288  3.0271342  4.4806184  3.5219965
## 188  3.4783188  2.9962957  3.3518939  3.3137480  3.7784933  3.1038993
## 189  3.9635499  3.2387015  3.7737206  3.6461253  3.9804954  3.3245860
## 190  3.3479929  3.3180182  3.3760589  3.5340208  4.2558129  3.4778128
## 191  4.0590774  3.7606912  4.0704819  4.1728718  4.7032040  3.9068454
## 192  4.1064740  3.6202402  3.9863660  3.9144320  4.3076125  3.6267052
## 193  3.9285619  3.8673993  3.9645048  4.1297254  4.8344204  4.0310348
## 194  4.5706048  4.0532491  4.5385811  4.5206125  4.8577017  4.1175880
## 195  4.5562227  3.9201675  4.4291868  4.3227473  4.5951927  3.9364135
## 196  4.6568232  5.2139619  4.9165074  5.3775098  6.3255912  5.5434422
## 197  5.2635422  5.2969040  5.3000795  5.3969453  5.9242754  5.3213187
## 198  5.3265408  5.2055704  5.3473657  5.3544294  5.6577022  5.1084781
## 199  5.1799849  5.2198431  5.2365508  5.3360908  5.8145404  5.2210869
##            187        188        189        190        191        192
## 2                                                                    
## 3                                                                    
## 4                                                                    
## 5                                                                    
## 6                                                                    
## 7                                                                    
## 8                                                                    
## 9                                                                    
## 10                                                                   
## 11                                                                   
## 12                                                                   
## 13                                                                   
## 14                                                                   
## 15                                                                   
## 16                                                                   
## 17                                                                   
## 18                                                                   
## 19                                                                   
## 20                                                                   
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## 29                                                                   
## 30                                                                   
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## 32                                                                   
## 33                                                                   
## 34                                                                   
## 35                                                                   
## 36                                                                   
## 37                                                                   
## 38                                                                   
## 39                                                                   
## 40                                                                   
## 41                                                                   
## 42                                                                   
## 43                                                                   
## 44                                                                   
## 45                                                                   
## 46                                                                   
## 47                                                                   
## 48                                                                   
## 49                                                                   
## 50                                                                   
## 51                                                                   
## 52                                                                   
## 53                                                                   
## 54                                                                   
## 55                                                                   
## 56                                                                   
## 57                                                                   
## 58                                                                   
## 59                                                                   
## 60                                                                   
## 61                                                                   
## 62                                                                   
## 63                                                                   
## 64                                                                   
## 65                                                                   
## 66                                                                   
## 67                                                                   
## 68                                                                   
## 69                                                                   
## 70                                                                   
## 71                                                                   
## 72                                                                   
## 73                                                                   
## 74                                                                   
## 75                                                                   
## 76                                                                   
## 77                                                                   
## 78                                                                   
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## 185                                                                  
## 186                                                                  
## 187                                                                  
## 188  3.6529691                                                       
## 189  4.0273423  0.7627074                                            
## 190  3.3416208  0.7776852  1.1257800                                 
## 191  3.7737122  1.5975146  1.3550515  1.1901887                      
## 192  4.1119167  1.3701751  0.9532788  1.2473386  0.8487339           
## 193  3.6577647  1.6560222  1.4822392  1.0871750  0.5048953  0.9447240
## 194  4.3937640  2.0021659  1.6196860  1.8804837  1.4339178  1.4020917
## 195  4.5038700  1.9096637  1.4661027  1.9131554  1.5492492  1.2895513
## 196  4.0962514  3.2759856  3.4662749  2.7252369  2.7334103  3.2641811
## 197  5.1898414  2.7689827  2.6689508  2.4393158  2.2250531  2.2413066
## 198  5.3928910  2.7330713  2.6352406  2.5546618  2.3388269  2.2503664
## 199  5.1354783  2.7414862  2.7117280  2.4261237  2.2363985  2.2844079
##            193        194        195        196        197        198
## 2                                                                    
## 3                                                                    
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## 193                                                                  
## 194  1.5660102                                                       
## 195  1.6837099  0.5164301                                            
## 196  2.5878066  2.9435501  3.1832382                                 
## 197  2.1315107  2.1022594  2.1501618  2.3737679                      
## 198  2.3837753  2.1578051  2.1128147  2.8690217  0.8944064           
## 199  2.1931853  2.1888695  2.2355320  2.3353797  0.4144272  0.7270761
##            199        200        201        202        203        204
## 2                                                                    
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##  [ reached getOption("max.print") -- omitted 307 rows ]
# look at the summary of the distances

summary(dist_eu)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.1343  3.4625  4.8241  4.9111  6.1863 14.3970

then run k-means algorithm on the dataset and investigate what is the optimal number of clusters and run the algorithm again.

km <-kmeans(Boston_scaled, centers = 3)


# plot the dataset with clusters
pairs(Boston_scaled[6:10], col = km$cluster)

set.seed(123)

# determine the number of clusters
k_max <- 10

# calculate the total within sum of squares
twcss <- sapply(1:k_max, function(k){kmeans(Boston_scaled, k)$tot.withinss})

# visualize the results
qplot(x = 1:k_max, y = twcss, geom = 'line')

# The optimal number of clusters is when the value of total WCSS changes radically. In this case, two clusters would seem optimal 

km <-kmeans(Boston_scaled, centers = 2)

pairs(Boston_scaled, col = km$cluster)


Dimensionality reduction techniques

In this part we will analyse a data set named humanW, it originates from the United Nations Development Programme. See their data page for more information. For a nice overview see also the calculating the human development indices pdf. Most of the variable names in the data have been shortened and two new variables have been computed. See the meta file. For the modified data please check our renamed variables and wrangled raw data, as well as R script for data wrangling.

Now, let’s have a look on our data set, the data now have 155 observations and 8 variables.

humanW <- read.csv(file =  "C:/Users/ahmed/Desktop/IODS-project/data/human.csv")
row.names(humanW) <- humanW$X
humanW <- humanW[-1]
dim(humanW)
## [1] 155   8

Graphical overview of the data and summaries of the variables.

library(ggplot2)
library(GGally)
library(dplyr)
library(corrplot)
p0 <- ggpairs(humanW)
p0

cor(humanW) %>% corrplot()

From the correlation matrix we can assume for example Proportion of females with at least secondary education is positively correlated with Life expectancy at birth and Expected years of schooling, whereas, it is negatively correlated with Maternal mortality ratio and Adolescent birth rate. We can see also Percetange of female representatives in parliament is very mildly correlated with Expected years of schooling. Most of the variables are normally destributed except for Maternal mortality ratio and Adolescent birth rate.

Principal component analysis (PCA) on the not standardized human data

pca_humanW1 <- prcomp(humanW)

# draw a biplot of the principal component representation and the original variables
biplot(pca_humanW1, choices = 1:2, cex = c(0.8, 1), col = c("grey40", "deeppink2"))

Principal component analysis (PCA) on the standardized human data

# standardize the variables
humanW_std <- scale(humanW)
humanW_std
##                                           popu_sec_edu_fem
## Norway                                         1.358818869
## Australia                                      1.258589759
## Switzerland                                    1.281222139
## Denmark                                        1.297388124
## Netherlands                                    1.045198751
## Germany                                        1.323253701
## Ireland                                        0.812408561
## United States                                  1.284455336
## Canada                                         1.442881993
## New Zealand                                    1.281222139
## Singapore                                      0.605483947
## Sweden                                         1.006400386
## United Kingdom                                 1.436415599
## Iceland                                        1.151894255
## Korea (Republic of)                            0.699246663
## Israel                                         0.938503247
## Luxembourg                                     1.442881993
## Japan                                          1.022566372
## Belgium                                        0.715412648
## France                                         0.731578634
## Austria                                        1.442881993
## Finland                                        1.442881993
## Slovenia                                       1.307087715
## Spain                                          0.369460560
## Italy                                          0.511721232
## Czech Republic                                 1.439648796
## Greece                                         0.133437173
## Estonia                                        1.442881993
## Cyprus                                         0.666914692
## Qatar                                          0.366227363
## Slovakia                                       1.413783219
## Poland                                         0.776843393
## Lithuania                                      1.090463510
## Malta                                          0.427658108
## Saudi Arabia                                   0.165769144
## Argentina                                      0.029974866
## United Arab Emirates                           0.573151977
## Chile                                          0.579618371
## Portugal                                      -0.248080084
## Hungary                                        1.374984854
## Bahrain                                        0.042907654
## Latvia                                         1.407316825
## Croatia                                        0.957902430
## Kuwait                                         0.007342486
## Montenegro                                     0.932036853
## Belarus                                        1.022566372
## Russian Federation                             1.106629496
## Oman                                          -0.264246069
## Romania                                        0.993467598
## Uruguay                                       -0.031455879
## Bahamas                                        1.158360649
## Kazakhstan                                     1.290921730
## Barbados                                       1.103396299
## Bulgaria                                       1.216558197
## Panama                                        -0.044388667
## Malaysia                                       0.314496210
## Mauritius                                     -0.193115733
## Trinidad and Tobago                            0.139903567
## Serbia                                         0.097872005
## Cuba                                           0.611950342
## Lebanon                                       -0.076720638
## Costa Rica                                    -0.151084171
## Iran (Islamic Republic of)                     0.220733494
## Venezuela (Bolivarian Republic of)             0.039674457
## Turkey                                        -0.529368230
## Sri Lanka                                      0.560219188
## Mexico                                         0.010575683
## Brazil                                        -0.024989485
## Georgia                                        1.109862693
## Azerbaijan                                     1.239190576
## Jordan                                         0.456756881
## The former Yugoslav Republic of Macedonia     -0.490569865
## Ukraine                                        1.174526635
## Algeria                                       -0.927051472
## Peru                                           0.029974866
## Albania                                        0.854440123
## Armenia                                        1.248890168
## Bosnia and Herzegovina                        -0.338609602
## Ecuador                                       -0.493803062
## China                                          0.107571596
## Fiji                                           0.285397436
## Mongolia                                       0.967602021
## Thailand                                      -0.636063734
## Libya                                          0.004109289
## Tunisia                                       -0.729826450
## Colombia                                       0.049374048
## Jamaica                                        0.602250750
## Tonga                                          1.038732357
## Belize                                         0.679847480
## Dominican Republic                             0.007342486
## Suriname                                      -0.348309193
## Maldives                                      -0.907652289
## Samoa                                          0.288630633
## Botswana                                       0.589317962
## Moldova (Republic of)                          1.235957379
## Egypt                                         -0.370941573
## Gabon                                         -0.047621864
## Indonesia                                     -0.500269456
## Paraguay                                      -0.600498566
## Philippines                                    0.340361786
## El Salvador                                   -0.600498566
## South Africa                                   0.560219188
## Viet Nam                                       0.130203976
## Bolivia (Plurinational State of)              -0.251313281
## Kyrgyzstan                                     1.265056153
## Iraq                                          -0.891486304
## Guyana                                         0.159302749
## Nicaragua                                     -0.516435442
## Morocco                                       -1.121043297
## Namibia                                       -0.713660464
## Guatemala                                     -1.082244932
## Tajikistan                                     1.284455336
## India                                         -0.917351881
## Honduras                                      -0.885019910
## Bhutan                                        -0.691028085
## Syrian Arab Republic                          -0.836521953
## Congo                                         -0.506735851
## Zambia                                        -0.956150246
## Ghana                                         -0.328910011
## Bangladesh                                    -0.687794887
## Cambodia                                      -1.470228583
## Kenya                                         -0.972316231
## Nepal                                         -1.218039210
## Pakistan                                      -1.166308056
## Myanmar                                       -1.049912961
## Swaziland                                     -1.082244932
## Tanzania (United Republic of)                 -1.609256057
## Cameroon                                      -1.101644115
## Zimbabwe                                      -0.215748113
## Mauritania                                    -1.521959736
## Papua New Guinea                              -1.544592116
## Yemen                                         -1.512260145
## Lesotho                                       -1.082244932
## Togo                                          -1.269770363
## Haiti                                         -1.066078947
## Rwanda                                        -1.531659327
## Uganda                                        -1.049912961
## Benin                                         -1.424963823
## Sudan                                         -1.399098247
## Senegal                                       -1.557524904
## Afghanistan                                   -1.599556466
## Côte d'Ivoire                                -1.337667502
## Malawi                                        -1.431430217
## Ethiopia                                      -1.538125721
## Gambia                                        -1.227738801
## Congo (Democratic Republic of the)            -1.376465867
## Liberia                                       -1.292402743
## Mali                                          -1.541358918
## Mozambique                                    -1.745050335
## Sierra Leone                                  -1.466995385
## Burkina Faso                                  -1.761216320
## Burundi                                       -1.618955649
## Chad                                          -1.735350744
## Central African Republic                      -1.463762188
## Niger                                         -1.712718364
##                                           lab_force_partic_femal
## Norway                                               0.541064622
## Australia                                            0.391483737
## Switzerland                                          0.578459844
## Denmark                                              0.385251200
## Netherlands                                          0.372786126
## Germany                                              0.067391818
## Ireland                                              0.036229134
## United States                                        0.235670314
## Canada                                               0.565994770
## New Zealand                                          0.590924917
## Singapore                                            0.391483737
## Sweden                                               0.484971790
## United Kingdom                                       0.198275093
## Iceland                                              1.120690554
## Korea (Republic of)                                 -0.150746973
## Israel                                               0.335390905
## Luxembourg                                          -0.113351752
## Japan                                               -0.231769953
## Belgium                                             -0.312792932
## France                                              -0.113351752
## Austria                                              0.129717187
## Finland                                              0.198275093
## Slovenia                                            -0.013631161
## Spain                                               -0.001166088
## Italy                                               -0.805163347
## Czech Republic                                      -0.088421604
## Greece                                              -0.518466650
## Estonia                                              0.229437778
## Cyprus                                               0.216972704
## Qatar                                               -0.107119215
## Slovakia                                            -0.088421604
## Poland                                              -0.225537416
## Lithuania                                            0.204507630
## Malta                                               -0.911116474
## Saudi Arabia                                        -2.014275505
## Argentina                                           -0.312792932
## United Arab Emirates                                -0.375118301
## Chile                                               -0.206839805
## Portugal                                             0.148414798
## Hungary                                             -0.481071428
## Bahrain                                             -0.830093495
## Latvia                                               0.148414798
## Croatia                                             -0.487303965
## Kuwait                                              -0.555861871
## Montenegro                                          -0.593257093
## Belarus                                             -0.150746973
## Russian Federation                                   0.285530610
## Oman                                                -1.465812258
## Romania                                             -0.238002490
## Uruguay                                              0.192042556
## Bahamas                                              1.045900111
## Kazakhstan                                           0.946179521
## Barbados                                             0.833993856
## Bulgaria                                            -0.287862785
## Panama                                              -0.219304879
## Malaysia                                            -0.506001576
## Mauritius                                           -0.555861871
## Trinidad and Tobago                                  0.029996597
## Serbia                                              -0.499769039
## Cuba                                                -0.568326945
## Lebanon                                             -1.821066861
## Costa Rica                                          -0.368885764
## Iran (Islamic Republic of)                          -2.238646833
## Venezuela (Bolivarian Republic of)                  -0.088421604
## Turkey                                              -1.440882110
## Sri Lanka                                           -1.085627507
## Mexico                                              -0.462373818
## Brazil                                               0.428878958
## Georgia                                              0.248135388
## Azerbaijan                                           0.647017750
## Jordan                                              -2.300972202
## The former Yugoslav Republic of Macedonia           -0.587024556
## Ukraine                                              0.042461671
## Algeria                                             -2.325902349
## Peru                                                 0.977342205
## Albania                                             -0.474838892
## Armenia                                              0.104787040
## Bosnia and Herzegovina                              -1.147952876
## Ecuador                                              0.135949724
## China                                                0.709343118
## Fiji                                                -0.936046622
## Mongolia                                             0.254367925
## Thailand                                             0.734273266
## Libya                                               -1.403486889
## Tunisia                                             -1.708881197
## Colombia                                             0.204507630
## Jamaica                                              0.223205241
## Tonga                                                0.061159281
## Belize                                              -0.206839805
## Dominican Republic                                  -0.075956530
## Suriname                                            -0.749070515
## Maldives                                             0.229437778
## Samoa                                               -1.808601787
## Botswana                                             1.207946070
## Moldova (Republic of)                               -0.929814085
## Egypt                                               -1.796136713
## Gabon                                                0.229437778
## Indonesia                                           -0.069723993
## Paraguay                                             0.198275093
## Philippines                                         -0.088421604
## El Salvador                                         -0.294095322
## South Africa                                        -0.499769039
## Viet Nam                                             1.276503976
## Bolivia (Plurinational State of)                     0.728040729
## Kyrgyzstan                                           0.216972704
## Iraq                                                -2.344599960
## Guyana                                              -0.618187240
## Nicaragua                                           -0.319025469
## Morocco                                             -1.621625680
## Namibia                                              0.135949724
## Guatemala                                           -0.200607268
## Tajikistan                                           0.397716274
## India                                               -1.590462996
## Honduras                                            -0.605722166
## Bhutan                                               0.883854152
## Syrian Arab Republic                                -2.431855477
## Congo                                                0.996039816
## Zambia                                               1.282736513
## Ghana                                                0.921249373
## Bangladesh                                           0.304228220
## Cambodia                                             1.637991116
## Kenya                                                0.603389991
## Nepal                                                1.706549022
## Pakistan                                            -1.740043881
## Myanmar                                              1.413619788
## Swaziland                                           -0.537164261
## Tanzania (United Republic of)                        2.217617047
## Cameroon                                             0.703110582
## Zimbabwe                                             1.912222739
## Mauritania                                          -1.484509869
## Papua New Guinea                                     1.120690554
## Yemen                                               -1.690183586
## Lesotho                                              0.403948811
## Togo                                                 1.750176780
## Haiti                                                0.522367012
## Rwanda                                               2.111663920
## Uganda                                               1.451015009
## Benin                                                0.939946984
## Sudan                                               -1.322463909
## Senegal                                              0.840226393
## Afghanistan                                         -2.288507128
## Côte d'Ivoire                                      -0.007398624
## Malawi                                               1.999478256
## Ethiopia                                             1.600595894
## Gambia                                               1.226643681
## Congo (Democratic Republic of the)                   1.133155627
## Liberia                                              0.354088515
## Mali                                                -0.107119215
## Mozambique                                           2.055571088
## Sierra Leone                                         0.821528783
## Burkina Faso                                         1.532037989
## Burundi                                              1.918455276
## Chad                                                 0.715575655
## Central African Republic                             1.251573828
## Niger                                               -0.780233199
##                                           exp_year_edu life_exp_birth
## Norway                                     1.522355407    1.193756093
## Australia                                  2.472975726    1.289770723
## Switzerland                                0.923816688    1.361781696
## Denmark                                    1.944853327    1.025730490
## Netherlands                                1.663188047    1.193756093
## Germany                                    1.170273807    1.109743291
## Ireland                                    1.909645167    1.109743291
## United States                              1.170273807    0.893710373
## Canada                                     0.959024848    1.241763408
## New Zealand                                2.120894126    1.217759750
## Singapore                                  0.782984048    1.361781696
## Sweden                                     0.923816688    1.265767066
## United Kingdom                             1.064649327    1.085739634
## Iceland                                    2.050477807    1.313774381
## Korea (Republic of)                        1.311106447    1.229761579
## Israel                                     0.994233008    1.289770723
## Luxembourg                                 0.254861648    1.205757922
## Japan                                      0.747775888    1.421790840
## Belgium                                    1.099857487    1.097741463
## France                                     0.994233008    1.265767066
## Austria                                    0.888608528    1.169752435
## Finland                                    1.381522767    1.097741463
## Slovenia                                   1.275898287    1.049734147
## Spain                                      1.451939087    1.313774381
## Italy                                      0.994233008    1.373783525
## Czech Republic                             1.135065647    0.833701229
## Greece                                     1.557563567    1.109743291
## Estonia                                    1.170273807    0.617668311
## Cyprus                                     0.290069808    1.025730490
## Qatar                                      0.219653488    0.785693914
## Slovakia                                   0.677359568    0.557659167
## Poland                                     0.818192208    0.689679284
## Lithuania                                  1.135065647    0.197604304
## Malta                                      0.430902448    1.073737805
## Saudi Arabia                               1.099857487    0.317622591
## Argentina                                  1.663188047    0.557659167
## United Arab Emirates                       0.043612688    0.641671969
## Chile                                      0.712567728    1.205757922
## Portugal                                   1.099857487    1.109743291
## Hungary                                    0.782984048    0.425639051
## Bahrain                                    0.430902448    0.593664654
## Latvia                                     0.712567728    0.305620763
## Croatia                                    0.571735088    0.677677455
## Kuwait                                     0.536526928    0.329624420
## Montenegro                                 0.712567728    0.545657338
## Belarus                                    0.888608528   -0.042432272
## Russian Federation                         0.536526928   -0.186454218
## Oman                                       0.149237168    0.617668311
## Romania                                    0.360486128    0.365629907
## Uruguay                                    0.818192208    0.665675626
## Bahamas                                   -0.202844431    0.449642708
## Kazakhstan                                 0.642151408   -0.270467019
## Barbados                                   0.782984048    0.473646366
## Bulgaria                                   0.430902448    0.305620763
## Panama                                     0.043612688    0.713682941
## Malaysia                                  -0.167636271    0.365629907
## Mauritius                                  0.853400368    0.329624420
## Trinidad and Tobago                       -0.308468911   -0.150448731
## Serbia                                     0.430902448    0.389633564
## Cuba                                       0.219653488    0.929715860
## Lebanon                                    0.219653488    0.917714031
## Costa Rica                                 0.254861648    0.929715860
## Iran (Islamic Republic of)                 0.677359568    0.449642708
## Venezuela (Bolivarian Republic of)         0.360486128    0.305620763
## Turkey                                     0.466110608    0.437640879
## Sri Lanka                                  0.184445328    0.389633564
## Mexico                                    -0.026803631    0.617668311
## Brazil                                     0.712567728    0.341626249
## Georgia                                    0.219653488    0.389633564
## Azerbaijan                                -0.449301551   -0.102441416
## Jordan                                     0.114029008    0.281617105
## The former Yugoslav Republic of Macedonia  0.078820848    0.449642708
## Ukraine                                    0.677359568   -0.078437758
## Algeria                                    0.290069808    0.377631735
## Peru                                      -0.026803631    0.353628078
## Albania                                   -0.484509711    0.737686599
## Armenia                                   -0.308468911    0.365629907
## Bosnia and Herzegovina                     0.149237168    0.581662825
## Ecuador                                    0.360486128    0.509651852
## China                                     -0.026803631    0.497650023
## Fiji                                       0.888608528   -0.198456046
## Mongolia                                   0.501318768   -0.270467019
## Thailand                                   0.114029008    0.329624420
## Libya                                      0.290069808   -0.006426786
## Tunisia                                    0.501318768    0.377631735
## Colombia                                   0.114029008    0.281617105
## Jamaica                                   -0.273260751    0.485648194
## Tonga                                      0.536526928    0.137595160
## Belize                                     0.149237168   -0.198456046
## Dominican Republic                        -0.026803631    0.221607961
## Suriname                                  -0.167636271   -0.066435930
## Maldives                                  -0.062011791    0.617668311
## Samoa                                     -0.097219951    0.209606132
## Botswana                                  -0.238052591   -0.858556630
## Moldova (Republic of)                     -0.449301551   -0.006426786
## Egypt                                      0.114029008   -0.066435930
## Gabon                                     -0.238052591   -0.870558458
## Indonesia                                 -0.062011791   -0.330476163
## Paraguay                                  -0.449301551    0.149596988
## Philippines                               -0.660550511   -0.414488964
## El Salvador                               -0.308468911    0.161598817
## South Africa                               0.149237168   -1.710686473
## Viet Nam                                  -0.449301551    0.497650023
## Bolivia (Plurinational State of)           0.008404529   -0.402487136
## Kyrgyzstan                                -0.238052591   -0.126445074
## Iraq                                      -1.083048430   -0.270467019
## Guyana                                    -1.012632111   -0.630521883
## Nicaragua                                 -0.590134191    0.389633564
## Morocco                                   -0.554926031    0.281617105
## Namibia                                   -0.660550511   -0.822551143
## Guatemala                                 -0.871799471    0.017576872
## Tajikistan                                -0.695758671   -0.270467019
## India                                     -0.519717871   -0.438492622
## Honduras                                  -0.730966831    0.173600646
## Bhutan                                    -0.202844431   -0.258465190
## Syrian Arab Republic                      -0.308468911   -0.246463361
## Congo                                     -0.730966831   -1.122596863
## Zambia                                     0.114029008   -1.386637096
## Ghana                                     -0.590134191   -1.230613322
## Bangladesh                                -1.118256590   -0.006426786
## Cambodia                                  -0.801383151   -0.390485307
## Kenya                                     -0.766174991   -1.206609664
## Nepal                                     -0.273260751   -0.246463361
## Pakistan                                  -1.892836110   -0.654525540
## Myanmar                                   -1.611170830   -0.690531027
## Swaziland                                 -0.660550511   -2.718840091
## Tanzania (United Republic of)             -1.399921870   -0.798547486
## Cameroon                                  -0.977423951   -1.938721220
## Zimbabwe                                  -0.801383151   -1.698684645
## Mauritania                                -1.646378990   -1.026582233
## Papua New Guinea                          -1.153464750   -1.086591376
## Yemen                                     -1.399921870   -0.942569431
## Lesotho                                   -0.730966831   -2.622825461
## Togo                                      -0.343677071   -1.434644411
## Haiti                                     -1.575962670   -1.062587719
## Rwanda                                    -1.012632111   -0.894562116
## Uganda                                    -1.188672910   -1.578666357
## Benin                                     -0.730966831   -1.446646240
## Sudan                                     -2.174501389   -0.978574917
## Senegal                                   -1.857627950   -0.618520054
## Afghanistan                               -1.364713710   -1.350631610
## Côte d'Ivoire                            -1.505546350   -2.418794372
## Malawi                                    -0.836591311   -1.062587719
## Ethiopia                                  -1.646378990   -0.906563945
## Gambia                                    -1.540754510   -1.374635267
## Congo (Democratic Republic of the)        -1.188672910   -1.554662699
## Liberia                                   -1.294297390   -1.290622466
## Mali                                      -1.681587150   -1.638675501
## Mozambique                                -1.364713710   -1.986728535
## Sierra Leone                              -1.611170830   -2.490805344
## Burkina Faso                              -1.892836110   -1.554662699
## Burundi                                   -1.083048430   -1.794699275
## Chad                                      -2.033668750   -2.406792543
## Central African Republic                  -2.104085069   -2.514809002
## Niger                                     -2.737831949   -1.230613322
##                                                    GNI         MMR
## Norway                                     1.229380770 -0.68503778
## Australia                                  0.662854003 -0.67559445
## Switzerland                                1.046630200 -0.67559445
## Denmark                                    0.735954231 -0.68031611
## Netherlands                                0.754229288 -0.67559445
## Germany                                    0.699404117 -0.67087278
## Ireland                                    0.516653547 -0.66142944
## United States                              1.010080086 -0.57171776
## Canada                                     0.644578946 -0.65198611
## New Zealand                                0.333902977 -0.66615111
## Singapore                                  1.485231568 -0.67559445
## Sweden                                     0.772504345 -0.68503778
## United Kingdom                             0.498378490 -0.66615111
## Iceland                                    0.407003205 -0.68503778
## Korea (Republic of)                        0.370453091 -0.57643943
## Israel                                     0.297352863 -0.69448112
## Luxembourg                                 1.064905257 -0.65198611
## Japan                                      0.425278262 -0.67559445
## Belgium                                    0.626303889 -0.67559445
## France                                     0.443553319 -0.64726444
## Austria                                    0.681129060 -0.68503778
## Finland                                    0.480103433 -0.68503778
## Slovenia                                   0.004951951 -0.67087278
## Spain                                      0.315627920 -0.68503778
## Italy                                      0.352178034 -0.68503778
## Czech Republic                            -0.013323106 -0.68031611
## Greece                                    -0.104698391 -0.68031611
## Estonia                                   -0.086423334 -0.65198611
## Cyprus                                     0.041502065 -0.65670778
## Qatar                                     -1.128101583 -0.67559445
## Slovakia                                  -0.049873220 -0.67087278
## Poland                                    -0.159523562 -0.68975945
## Lithuania                                 -0.122973448 -0.65198611
## Malta                                      0.023227008 -0.66142944
## Saudi Arabia                               0.991805029 -0.62837777
## Argentina                                 -0.250898847 -0.37812940
## United Arab Emirates                       1.211105713 -0.66615111
## Chile                                     -0.287448961 -0.60004777
## Portugal                                  -0.068148277 -0.66615111
## Hungary                                   -0.177798619 -0.63782111
## Bahrain                                    0.461828376 -0.60004777
## Latvia                                    -0.232623790 -0.64254277
## Croatia                                   -0.616399987 -0.64254277
## Kuwait                                     1.576606853 -0.63782111
## Montenegro                                -0.963626070 -0.67087278
## Belarus                                   -0.726050329 -0.69920278
## Russian Federation                        -0.214348733 -0.59060443
## Oman                                       0.388728148 -0.65198611
## Romania                                   -0.689500215 -0.54810943
## Uruguay                                   -0.634675044 -0.63782111
## Bahamas                                   -0.269173904 -0.52922276
## Kazakhstan                                -0.323999075 -0.58116110
## Barbados                                  -1.182926754 -0.45839775
## Bulgaria                                  -0.890525842 -0.68031611
## Panama                                    -0.671225158 -0.30258272
## Malaysia                                  -0.196073676 -0.56699610
## Mauritius                                 -0.707775272 -0.35924273
## Trinidad and Tobago                       -0.031598163 -0.30730439
## Serbia                                    -1.219476868 -0.62837777
## Cuba                                       1.302480998 -0.32619106
## Lebanon                                   -0.762600443 -0.62837777
## Costa Rica                                -1.055001355 -0.52450109
## Iran (Islamic Republic of)                -0.908800899 -0.59532610
## Venezuela (Bolivarian Republic of)        -0.817425614 -0.18454104
## Turkey                                    -0.652950101 -0.60949110
## Sri Lanka                                  1.649707081 -0.56699610
## Mexico                                    -0.835700671 -0.47256275
## Brazil                                    -0.927075956 -0.37812940
## Georgia                                    1.265930884 -0.51033609
## Azerbaijan                                -0.780875500 -0.58116110
## Jordan                                    -1.329127210 -0.46784108
## The former Yugoslav Republic of Macedonia -1.292577096 -0.67087278
## Ukraine                                    1.540056739 -0.59532610
## Algeria                                   -1.109826526 -0.28369605
## Peru                                      -1.347402267 -0.28369605
## Albania                                    1.704532252 -0.60476944
## Armenia                                    1.521781682 -0.56699610
## Bosnia and Herzegovina                     1.613156967 -0.66615111
## Ecuador                                   -1.402227438 -0.29313939
## China                                     -1.164651697 -0.55283109
## Fiji                                       1.357306169 -0.42534607
## Mongolia                                  -1.383952381 -0.38285107
## Thailand                                  -1.073276412 -0.58116110
## Libya                                     -0.945351013 -0.63309944
## Tunisia                                   -1.438777552 -0.48672775
## Colombia                                  -1.256026982 -0.31202606
## Jamaica                                    1.339031112 -0.32619106
## Tonga                                      0.790779402 -0.13732436
## Belize                                     1.375581226 -0.49144942
## Dominican Republic                        -1.274302039 -0.23175771
## Suriname                                  -0.872250785 -0.09010769
## Maldives                                  -1.201201811 -0.55755276
## Samoa                                      0.845604573 -0.43006774
## Botswana                                  -0.744325386  0.09875900
## Moldova (Republic of)                      0.827329516 -0.60476944
## Egypt                                     -1.420502495 -0.49144942
## Gabon                                     -0.799150557  0.42927572
## Indonesia                                  1.667982138  0.19319235
## Paraguay                                   1.393856283 -0.18454104
## Philippines                                1.412131340 -0.13732436
## El Salvador                                1.320756055 -0.37812940
## South Africa                              -1.237751925 -0.04289102
## Viet Nam                                   0.809054459 -0.47256275
## Bolivia (Plurinational State of)           0.973529972  0.24040903
## Kyrgyzstan                                 0.059777122 -0.34979940
## Iraq                                      -1.018451241 -0.38757274
## Guyana                                     1.138005485  0.47649239
## Nicaragua                                  0.534928604 -0.23175771
## Morocco                                    1.174555599 -0.13732436
## Namibia                                    1.594881910 -0.09010769
## Guatemala                                  1.192830656 -0.04289102
## Tajikistan                                -0.470199531 -0.49617109
## India                                      0.900429744  0.19319235
## Honduras                                   0.279077806 -0.13732436
## Bhutan                                     1.284205941 -0.13732436
## Syrian Arab Republic                      -0.451924474 -0.47256275
## Congo                                      1.101455371  1.23195918
## Zambia                                     0.224252635  0.61814242
## Ghana                                      0.260802749  1.09030915
## Bangladesh                                 0.096327236  0.09875900
## Cambodia                                  -0.378824246  0.09875900
## Kenya                                     -0.433649417  1.18474250
## Nepal                                     -0.561574816  0.19319235
## Pakistan                                   0.608028832  0.09875900
## Myanmar                                    0.553203661  0.24040903
## Swaziland                                  0.918704801  0.75979244
## Tanzania (United Republic of)             -0.525024702  1.23195918
## Cameroon                                  -0.415374360  2.08185930
## Zimbabwe                                  -1.530152837  1.51525922
## Mauritania                                 0.205977578  0.80700911
## Papua New Guinea                          -0.488474588  0.33484237
## Yemen                                      0.187702521  0.57092574
## Lesotho                                    0.132877350  1.60969257
## Togo                                      -1.731178464  1.42082587
## Haiti                                     -1.511877780  1.09030915
## Rwanda                                    -1.639803179  0.80700911
## Uganda                                    -1.548427894  0.99587581
## Benin                                     -1.493602723  0.90144246
## Sudan                                      0.242527692  0.99587581
## Senegal                                   -0.579849873  0.80700911
## Afghanistan                               -1.457052609  1.18474250
## Côte d'Ivoire                             0.078052179  2.69567606
## Malawi                                     1.448681454  1.70412591
## Ethiopia                                  -1.676353293  1.27917585
## Gambia                                    -1.621528122  1.32639252
## Congo (Democratic Republic of the)         1.247655827  2.74289274
## Liberia                                    1.558331796  2.31794267
## Mali                                      -1.584978008  1.89299261
## Mozambique                                -1.767728578  1.56247589
## Sierra Leone                              -1.475327666  4.48990967
## Burkina Faso                              -1.566702951  1.18474250
## Burundi                                    1.466956511  2.79010941
## Chad                                      -0.598124930  3.92330958
## Central African Republic                   1.083180314  3.45114284
## Niger                                      1.741082366  2.27072600
##                                                    ABR  parl_repres
## Norway                                    -0.957352128  1.626810626
## Australia                                 -0.852759925  0.834662185
## Switzerland                               -1.100862360  0.660563627
## Denmark                                   -1.023026302  1.487531779
## Netherlands                               -0.996270157  1.391777572
## Germany                                   -1.054647201  1.391777572
## Ireland                                   -0.947622621 -0.088060174
## United States                             -0.393040707 -0.131584814
## Canada                                    -0.794382882  0.634448843
## New Zealand                               -0.531686186  0.913006537
## Singapore                                 -1.001134911  0.382005934
## Sweden                                    -0.988973027  1.975007743
## United Kingdom                            -0.519524302  0.225317231
## Iceland                                   -0.867354186  1.774794401
## Korea (Republic of)                       -1.093565230 -0.401437579
## Israel                                    -0.957352128  0.138267952
## Luxembourg                                -0.945190244  0.643153771
## Japan                                     -1.015729172 -0.810569191
## Belgium                                   -0.984108273  1.870548608
## France                                    -1.008432041  0.416825645
## Austria                                   -1.047350070  0.817252330
## Finland                                   -0.923298853  1.879253536
## Slovenia                                  -1.132483259  0.590924204
## Spain                                     -0.889245577  1.487531779
## Italy                                     -1.049782447  0.799842474
## Czech Republic                            -1.027891056 -0.175109453
## Greece                                    -0.857624679  0.007694033
## Estonia                                   -0.738438215 -0.096765102
## Cyprus                                    -1.013296795 -0.732224840
## Qatar                                     -0.916001722 -1.820340830
## Slovakia                                  -0.760329606 -0.192519309
## Poland                                    -0.850327548  0.103448240
## Lithuania                                 -0.889245577  0.216612303
## Malta                                     -0.704384939 -0.688700200
## Saudi Arabia                              -0.898975085 -0.088060174
## Argentina                                  0.176135467  1.383072644
## United Arab Emirates                      -0.475741519 -0.296978444
## Chile                                      0.198026858 -0.444962219
## Portugal                                  -0.840598041  0.904301609
## Hungary                                   -0.852759925 -0.941143110
## Bahrain                                   -0.811409519 -0.514601642
## Latvia                                    -0.818706650 -0.253453805
## Croatia                                   -0.838165664  0.425530573
## Kuwait                                    -0.794382882 -1.689766911
## Montenegro                                -0.777356244 -0.314388300
## Belarus                                   -0.646007896  0.799842474
## Russian Federation                        -0.521956679 -0.558126282
## Oman                                      -0.889245577 -0.984667750
## Romania                                   -0.393040707 -0.775749480
## Uruguay                                    0.270998162 -0.819274119
## Bahamas                                   -0.453850128 -0.366617867
## Kazakhstan                                -0.419796852 -0.070650318
## Barbados                                   0.030192858 -0.114174958
## Bulgaria                                  -0.273854244 -0.044535534
## Panama                                     0.762338279 -0.140289742
## Malaysia                                  -1.008432041 -0.584241065
## Mauritius                                 -0.395473084 -0.810569191
## Trinidad and Tobago                       -0.300610389  0.329776366
## Serbia                                    -0.736005838  1.139334663
## Cuba                                      -0.098723113  2.436368923
## Lebanon                                   -0.855192302 -1.550488064
## Costa Rica                                 0.331807583  1.078400167
## Iran (Islamic Republic of)                -0.378446447 -1.550488064
## Venezuela (Bolivarian Republic of)         0.876659989 -0.340503084
## Turkey                                    -0.395473084 -0.566831210
## Sri Lanka                                 -0.736005838 -1.315455011
## Mexico                                     0.395049380  1.409187428
## Brazil                                     0.575045264 -0.984667750
## Georgia                                   -0.008725171 -0.836683975
## Azerbaijan                                -0.174126794 -0.462372075
## Jordan                                    -0.502497664 -0.810569191
## The former Yugoslav Republic of Macedonia -0.701952563  1.078400167
## Ukraine                                   -0.521956679 -0.793159336
## Algeria                                   -0.903839838  0.416825645
## Peru                                       0.086137525  0.120858096
## Albania                                   -0.774923867 -0.018420751
## Armenia                                   -0.487903403 -0.888913543
## Bosnia and Herzegovina                    -0.779788621 -0.140289742
## Ecuador                                    0.725852626  1.800909184
## China                                     -0.937893114  0.234022159
## Fiji                                      -0.106020244 -0.601650921
## Mongolia                                  -0.692223055 -0.523306570
## Thailand                                  -0.149803026 -1.289340227
## Libya                                     -1.086268099 -0.427552363
## Tunisia                                   -1.035188186  0.904301609
## Colombia                                   0.519100597 -0.001010895
## Jamaica                                    0.558018626 -0.366617867
## Tonga                                     -0.706817316 -1.820340830
## Belize                                     0.589639525 -0.662585417
## Dominican Republic                         1.275569786 -0.157699597
## Suriname                                  -0.290880881 -0.793159336
## Maldives                                  -1.044917693 -1.306750083
## Samoa                                     -0.458714881 -1.289340227
## Botswana                                  -0.071966968 -0.993372678
## Moldova (Republic of)                     -0.434391113 -0.009715823
## Egypt                                     -0.101155490 -1.628832416
## Gabon                                      1.358270598 -0.410142507
## Indonesia                                  0.027760481 -0.331798156
## Paraguay                                   0.482614945 -0.357912940
## Philippines                               -0.008725171  0.538694636
## El Salvador                                0.701528858  0.564809420
## South Africa                               0.091002278  1.722564833
## Viet Nam                                  -0.441688244  0.294956654
## Bolivia (Plurinational State of)           0.601801409  2.688811832
## Kyrgyzstan                                -0.434391113  0.207907375
## Iraq                                       0.523965351  0.486465069
## Guyana                                     1.005575960  0.904301609
## Nicaragua                                  1.304758308  1.583285986
## Morocco                                   -0.276286620 -0.862798759
## Namibia                                    0.188297351  1.461416996
## Guatemala                                  1.217192743 -0.662585417
## Tajikistan                                -0.106020244 -0.497191786
## India                                     -0.349257925 -0.758339624
## Honduras                                   0.896119003  0.425530573
## Bhutan                                    -0.152235403 -1.097831813
## Syrian Arab Republic                      -0.135208765 -0.740929768
## Congo                                      1.934743902 -0.819274119
## Zambia                                     1.903123004 -0.714814984
## Ghana                                      0.273430539 -0.871503687
## Bangladesh                                 0.813418192 -0.079355246
## Cambodia                                  -0.069534591 -0.166404525
## Kenya                                      1.129627177 -0.009715823
## Nepal                                      0.645584192  0.747612906
## Pakistan                                  -0.483038650 -0.105470030
## Myanmar                                   -0.852759925 -1.411209218
## Swaziland                                  0.604233786 -0.540716426
## Tanzania (United Republic of)              1.837448830  1.313433221
## Cameroon                                   1.669614830  0.538694636
## Zimbabwe                                   0.319645699  1.235088870
## Mauritania                                 0.635854684  0.112153168
## Papua New Guinea                           0.363428481 -1.585307776
## Yemen                                     -0.003860417 -1.759406335
## Lesotho                                    1.027467351  0.512579852
## Togo                                       1.078547264 -0.288273516
## Haiti                                     -0.125479258 -1.515668353
## Rwanda                                    -0.329798910  3.184992724
## Uganda                                     1.932311526  1.226383942
## Benin                                      1.046926366 -1.089126885
## Sudan                                      0.896119003  0.251432015
## Senegal                                    1.149086192  1.896663392
## Afghanistan                                0.964225554  0.582219276
## Côte d'Ivoire                             2.022309468 -1.019487461
## Malawi                                     2.375004106 -0.366617867
## Ethiopia                                   0.759905902  0.399415789
## Gambia                                     1.669614830 -1.002077606
## Congo (Democratic Republic of the)         2.143928308 -1.106536741
## Liberia                                    1.708532859 -0.888913543
## Mali                                       3.124176164 -0.993372678
## Mozambique                                 2.204737729  1.626810626
## Sierra Leone                               1.302325931 -0.740929768
## Burkina Faso                               1.659885323 -0.662585417
## Burundi                                   -0.410067345  1.217679014
## Chad                                       2.550135236 -0.523306570
## Central African Republic                   1.243948888 -0.732224840
## Niger                                      3.834430193 -0.662585417
## attr(,"scaled:center")
##       popu_sec_edu_fem lab_force_partic_femal           exp_year_edu 
##               55.37290               52.51871               13.17613 
##         life_exp_birth                    GNI                    MMR 
##               71.65355               98.72903              149.08387 
##                    ABR            parl_repres 
##               47.15871               20.91161 
## attr(,"scaled:scale")
##       popu_sec_edu_fem lab_force_partic_femal           exp_year_edu 
##              30.929138              16.044831               2.840251 
##         life_exp_birth                    GNI                    MMR 
##               8.332064              54.719392             211.789590 
##                    ABR            parl_repres 
##              41.112051              11.487746
# summaries of the standardized variables showing means equal to zero
summary(humanW_std)
##  popu_sec_edu_fem   lab_force_partic_femal  exp_year_edu    
##  Min.   :-1.76122   Min.   :-2.43186       Min.   :-2.7378  
##  1st Qu.:-0.91250   1st Qu.:-0.50289       1st Qu.:-0.6782  
##  Median : 0.03967   Median : 0.06116       Median : 0.1140  
##  Mean   : 0.00000   Mean   : 0.00000       Mean   : 0.0000  
##  3rd Qu.: 0.96275   3rd Qu.: 0.58469       3rd Qu.: 0.7126  
##  Max.   : 1.44288   Max.   : 2.21762       Max.   : 2.4730  
##  life_exp_birth         GNI                 MMR               ABR         
##  Min.   :-2.7188   Min.   :-1.767729   Min.   :-0.6992   Min.   :-1.1325  
##  1st Qu.:-0.6425   1st Qu.:-0.826563   1st Qu.:-0.6496   1st Qu.:-0.8394  
##  Median : 0.3056   Median : 0.004952   Median :-0.4726   Median :-0.3298  
##  Mean   : 0.0000   Mean   : 0.000000   Mean   : 0.0000   Mean   : 0.0000  
##  3rd Qu.: 0.6717   3rd Qu.: 0.818192   3rd Qu.: 0.1932   3rd Qu.: 0.6030  
##  Max.   : 1.4218   Max.   : 1.741082   Max.   : 4.4899   Max.   : 3.8344  
##   parl_repres     
##  Min.   :-1.8203  
##  1st Qu.:-0.7409  
##  Median :-0.1403  
##  Mean   : 0.0000  
##  3rd Qu.: 0.6127  
##  Max.   : 3.1850

Now, let’s perform PCA for the standerdized data

#perform principal component analysis (with the SVD method)
pca_humanW2 <- prcomp(humanW_std)

# draw a biplot of the principal component representation and the original variables
biplot(pca_humanW2, choices = 1:2, cex = c(0.8, 1), col = c("grey55", "deeppink4"))

from the previous plots we can see that Maternal mortality ratio and Adolescent birth rate are contributing most to the PC1 with strong positive correlation with each other; meanwhile, they are quite negatively correlated to Expected years of schooling, Life expectancy at birth and Proportion of females with at least secondary education. However, all previous variables are very weakly correlated to * Proportion of females in the labour force* and Percetange of female representatives in parliament which are (the later) contributing more to the PC2. Such interpretation goes well with the former correlation matrix and is not feasible in the first biplot without standerdizing the variables for comparison.

Analysing the first two principal component dimensions of the biplot

s <- summary(pca_humanW2)

# rounded percetanges of variance captured by each PC
pca_pr <- round(100*s$importance[2, ], digits = 1)

# print out the percentages of variance
pca_pr
##  PC1  PC2  PC3  PC4  PC5  PC6  PC7  PC8 
## 51.7 15.5 12.2  9.1  3.8  3.5  2.6  1.5
# create object pc_lab to be used as axis labels
paste0(names(pca_pr), " (", pca_pr, "%)")
## [1] "PC1 (51.7%)" "PC2 (15.5%)" "PC3 (12.2%)" "PC4 (9.1%)"  "PC5 (3.8%)" 
## [6] "PC6 (3.5%)"  "PC7 (2.6%)"  "PC8 (1.5%)"
pc_lab <- paste0(names(pca_pr), " (", pca_pr, "%)")
pc_lab
## [1] "PC1 (51.7%)" "PC2 (15.5%)" "PC3 (12.2%)" "PC4 (9.1%)"  "PC5 (3.8%)" 
## [6] "PC6 (3.5%)"  "PC7 (2.6%)"  "PC8 (1.5%)"
# draw a biplot
biplot(pca_humanW2, cex = c(0.8, 1), col = c("grey60", "deeppink2"), xlab = pc_lab[1], ylab = pc_lab[2])

Here we can see that most of the variation is accounted for by the first two principal components which indicates validity of analysis. As we referred earlier Maternal mortality ratio and Adolescent birth rate are the most important variables which are found to be highly predicting less educational oppurtunities and shorter life span of related subjects. However, * Proportion of females in the labour force* and Percetange of female representatives in parliament seem to be related to other players which are not among our study variables.

The tea dataset

library(FactoMineR)
## Warning: package 'FactoMineR' was built under R version 3.4.3
library(tidyr)
data(tea)
str(tea)
## 'data.frame':    300 obs. of  36 variables:
##  $ breakfast       : Factor w/ 2 levels "breakfast","Not.breakfast": 1 1 2 2 1 2 1 2 1 1 ...
##  $ tea.time        : Factor w/ 2 levels "Not.tea time",..: 1 1 2 1 1 1 2 2 2 1 ...
##  $ evening         : Factor w/ 2 levels "evening","Not.evening": 2 2 1 2 1 2 2 1 2 1 ...
##  $ lunch           : Factor w/ 2 levels "lunch","Not.lunch": 2 2 2 2 2 2 2 2 2 2 ...
##  $ dinner          : Factor w/ 2 levels "dinner","Not.dinner": 2 2 1 1 2 1 2 2 2 2 ...
##  $ always          : Factor w/ 2 levels "always","Not.always": 2 2 2 2 1 2 2 2 2 2 ...
##  $ home            : Factor w/ 2 levels "home","Not.home": 1 1 1 1 1 1 1 1 1 1 ...
##  $ work            : Factor w/ 2 levels "Not.work","work": 1 1 2 1 1 1 1 1 1 1 ...
##  $ tearoom         : Factor w/ 2 levels "Not.tearoom",..: 1 1 1 1 1 1 1 1 1 2 ...
##  $ friends         : Factor w/ 2 levels "friends","Not.friends": 2 2 1 2 2 2 1 2 2 2 ...
##  $ resto           : Factor w/ 2 levels "Not.resto","resto": 1 1 2 1 1 1 1 1 1 1 ...
##  $ pub             : Factor w/ 2 levels "Not.pub","pub": 1 1 1 1 1 1 1 1 1 1 ...
##  $ Tea             : Factor w/ 3 levels "black","Earl Grey",..: 1 1 2 2 2 2 2 1 2 1 ...
##  $ How             : Factor w/ 4 levels "alone","lemon",..: 1 3 1 1 1 1 1 3 3 1 ...
##  $ sugar           : Factor w/ 2 levels "No.sugar","sugar": 2 1 1 2 1 1 1 1 1 1 ...
##  $ how             : Factor w/ 3 levels "tea bag","tea bag+unpackaged",..: 1 1 1 1 1 1 1 1 2 2 ...
##  $ where           : Factor w/ 3 levels "chain store",..: 1 1 1 1 1 1 1 1 2 2 ...
##  $ price           : Factor w/ 6 levels "p_branded","p_cheap",..: 4 6 6 6 6 3 6 6 5 5 ...
##  $ age             : int  39 45 47 23 48 21 37 36 40 37 ...
##  $ sex             : Factor w/ 2 levels "F","M": 2 1 1 2 2 2 2 1 2 2 ...
##  $ SPC             : Factor w/ 7 levels "employee","middle",..: 2 2 4 6 1 6 5 2 5 5 ...
##  $ Sport           : Factor w/ 2 levels "Not.sportsman",..: 2 2 2 1 2 2 2 2 2 1 ...
##  $ age_Q           : Factor w/ 5 levels "15-24","25-34",..: 3 4 4 1 4 1 3 3 3 3 ...
##  $ frequency       : Factor w/ 4 levels "1/day","1 to 2/week",..: 1 1 3 1 3 1 4 2 3 3 ...
##  $ escape.exoticism: Factor w/ 2 levels "escape-exoticism",..: 2 1 2 1 1 2 2 2 2 2 ...
##  $ spirituality    : Factor w/ 2 levels "Not.spirituality",..: 1 1 1 2 2 1 1 1 1 1 ...
##  $ healthy         : Factor w/ 2 levels "healthy","Not.healthy": 1 1 1 1 2 1 1 1 2 1 ...
##  $ diuretic        : Factor w/ 2 levels "diuretic","Not.diuretic": 2 1 1 2 1 2 2 2 2 1 ...
##  $ friendliness    : Factor w/ 2 levels "friendliness",..: 2 2 1 2 1 2 2 1 2 1 ...
##  $ iron.absorption : Factor w/ 2 levels "iron absorption",..: 2 2 2 2 2 2 2 2 2 2 ...
##  $ feminine        : Factor w/ 2 levels "feminine","Not.feminine": 2 2 2 2 2 2 2 1 2 2 ...
##  $ sophisticated   : Factor w/ 2 levels "Not.sophisticated",..: 1 1 1 2 1 1 1 2 2 1 ...
##  $ slimming        : Factor w/ 2 levels "No.slimming",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ exciting        : Factor w/ 2 levels "exciting","No.exciting": 2 1 2 2 2 2 2 2 2 2 ...
##  $ relaxing        : Factor w/ 2 levels "No.relaxing",..: 1 1 2 2 2 2 2 2 2 2 ...
##  $ effect.on.health: Factor w/ 2 levels "effect on health",..: 2 2 2 2 2 2 2 2 2 2 ...
dim(tea)
## [1] 300  36
keep_ <- c("How", "how", "sugar", "where", "lunch", "healthy", "diuretic")
teaW <- dplyr::select(tea, one_of(keep_))

gather(teaW) %>% ggplot(aes(value)) + facet_wrap("key", scales = "free") + geom_bar() + theme(axis.text.x = element_text(angle = 45, hjust = 1, size = 8))
## Warning: attributes are not identical across measure variables;
## they will be dropped

then, let’s do Multiple Correspondence Analysis on the tea data

# multiple correspondence analysis
mca <- MCA(teaW, graph = FALSE)

# summary of the model
summary(mca)
## 
## Call:
## MCA(X = teaW, graph = FALSE) 
## 
## 
## Eigenvalues
##                        Dim.1   Dim.2   Dim.3   Dim.4   Dim.5   Dim.6
## Variance               0.235   0.221   0.185   0.162   0.158   0.134
## % of var.             14.944  14.076  11.802  10.327  10.047   8.538
## Cumulative % of var.  14.944  29.020  40.822  51.149  61.196  69.734
##                        Dim.7   Dim.8   Dim.9  Dim.10  Dim.11
## Variance               0.123   0.116   0.101   0.079   0.057
## % of var.              7.837   7.402   6.396   5.026   3.606
## Cumulative % of var.  77.571  84.973  91.369  96.394 100.000
## 
## Individuals (the 10 first)
##                       Dim.1    ctr   cos2    Dim.2    ctr   cos2    Dim.3
## 1                  | -0.537  0.409  0.410 | -0.234  0.082  0.078 |  0.177
## 2                  | -0.354  0.178  0.119 |  0.167  0.042  0.026 | -0.593
## 3                  | -0.311  0.137  0.164 | -0.029  0.001  0.001 | -0.617
## 4                  | -0.537  0.409  0.410 | -0.234  0.082  0.078 |  0.177
## 5                  | -0.356  0.179  0.147 | -0.212  0.068  0.052 | -0.263
## 6                  | -0.413  0.242  0.250 | -0.153  0.035  0.034 | -0.196
## 7                  | -0.413  0.242  0.250 | -0.153  0.035  0.034 | -0.196
## 8                  | -0.456  0.295  0.182 |  0.043  0.003  0.002 | -0.172
## 9                  |  0.315  0.141  0.051 |  0.516  0.400  0.137 |  0.543
## 10                 |  0.504  0.361  0.227 |  0.626  0.591  0.350 | -0.256
##                       ctr   cos2  
## 1                   0.057  0.045 |
## 2                   0.632  0.335 |
## 3                   0.684  0.646 |
## 4                   0.057  0.045 |
## 5                   0.124  0.080 |
## 6                   0.069  0.056 |
## 7                   0.069  0.056 |
## 8                   0.053  0.026 |
## 9                   0.531  0.152 |
## 10                  0.118  0.058 |
## 
## Categories (the 10 first)
##                        Dim.1     ctr    cos2  v.test     Dim.2     ctr
## alone              |  -0.102   0.409   0.019  -2.397 |  -0.232   2.254
## lemon              |   0.928   5.768   0.107   5.644 |   0.009   0.001
## milk               |  -0.247   0.776   0.016  -2.198 |   0.414   2.319
## other              |   0.525   0.504   0.009   1.597 |   2.094   8.496
## tea bag            |  -0.676  15.743   0.597 -13.363 |  -0.121   0.534
## tea bag+unpackaged |   0.622   7.369   0.176   7.263 |   0.850  14.636
## unpackaged         |   1.568  17.941   0.335  10.010 |  -1.650  21.100
## No.sugar           |   0.203   1.292   0.044   3.625 |   0.130   0.561
## sugar              |  -0.217   1.381   0.044  -3.625 |  -0.139   0.599
## chain store        |  -0.623  15.120   0.690 -14.368 |  -0.145   0.865
##                       cos2  v.test     Dim.3     ctr    cos2  v.test  
## alone                0.100  -5.461 |  -0.079   0.315   0.012  -1.868 |
## lemon                0.000   0.053 |   0.855   6.188   0.090   5.195 |
## milk                 0.045   3.687 |  -0.007   0.001   0.000  -0.062 |
## other                0.136   6.368 |  -1.367   4.317   0.058  -4.156 |
## tea bag              0.019  -2.389 |  -0.173   1.308   0.039  -3.424 |
## tea bag+unpackaged   0.330   9.934 |   0.436   4.594   0.087   5.096 |
## unpackaged           0.371 -10.536 |  -0.322   0.956   0.014  -2.054 |
## No.sugar             0.018   2.317 |  -0.544  11.799   0.317  -9.734 |
## sugar                0.018  -2.317 |   0.582  12.613   0.317   9.734 |
## chain store          0.037  -3.335 |  -0.103   0.524   0.019  -2.378 |
## 
## Categorical variables (eta2)
##                      Dim.1 Dim.2 Dim.3  
## How                | 0.123 0.202 0.140 |
## how                | 0.675 0.562 0.089 |
## sugar              | 0.044 0.018 0.317 |
## where              | 0.755 0.613 0.054 |
## lunch              | 0.013 0.037 0.066 |
## healthy            | 0.005 0.076 0.240 |
## diuretic           | 0.029 0.040 0.392 |
# visualize MCA
plot(mca, invisible=c("ind"),habillage = "quali" )

here for example we can see that drinking unpackaged tea is more similar to drinking tea in tea shops, as well as, drinking tea in both chain stores and tea shops is more related to drinking both bagged and unpackaged tea category.